research article comparison of fuzzy ahp and fuzzy topsis...

Research ArticleComparison of Fuzzy AHP and Fuzzy TOPSIS for RoadPavement Maintenance Prioritization MethodologicalExposition and Case Study

Yashon O Ouma J Opudo and S Nyambenya

Department of Civil and Structural Engineering Moi University PO Box 3900 Eldoret 30100 Kenya

Correspondence should be addressed to Yashon O Ouma yashon ohotmailcom

Received 30 April 2015 Revised 15 June 2015 Accepted 16 June 2015

Academic Editor Samer Madanat

Copyright copy 2015 Yashon O Ouma et al This is an open access article distributed under the Creative Commons AttributionLicense which permits unrestricted use distribution and reproduction in any medium provided the original work is properlycited

For road pavement maintenance and repairs prioritization a multiattribute approach that compares fuzzy Analytical HierarchyProcess (AHP) and fuzzy Technique for Order Preference by Ideal Situation (TOPSIS) is evaluated The pavement distress datawas collected through empirical condition surveys and rating by pavement experts In comparison to the crisp AHP the fuzzyAHP and fuzzy TOPSIS pairwise comparison techniques are considered to be more suitable for the subjective analysis of thepavement conditions for automatedmaintenance prioritization From the case study results four pavementmaintenance objectiveswere determined as road safety pavement surface preservation road operational status and standards and road aesthetics withcorresponding depreciating significance weights of 119882 = [037 031 022 010]119879 The top three maintenance functions wereidentified as Thin Hot Mix Asphalt (HMA) overlays resurfacing and slurry seals which were a result of pavement crackingpotholes raveling and patching while the bottom three were cape seal micro surfacing and fog seal The two methods gavenearly the same prioritization ranking In general the fuzzy AHP approach tended to overestimate the maintenance prioritizationranking as compared to the fuzzy TOPSIS

1 Introduction

Road pavement condition survey and assessment are animportant component in the decision making procedurein pavement management systems (PMS) The two mainreasons for the assessment of pavement condition are torecognize and prioritize maintenance requirements in spe-cific road sections and to identify the pavement networkconditions and if any the rehabilitation requirements [1] Inurban road maintenance and rehabilitation (MampR) projectsthe evaluation of road pavement conditions is the initial phasethat guarantees suitable and sustainable maintenance pro-grams [2]

For pavement MampR projects specific pavement mainte-nance management systems (PMMS) should be proposedas suitable systems for the improvement of the efficiencyof decision making Furthermore such systems should beable to provide feedbacks on the impacts of the decisions interms of short and long termmaintenance strategies and with

respect to cost-benefit analysis [3] A typical structure thatintegrates PMS PMMS and MampR is depicted in Figure 1

From Figure 1 it is seen that a PMS is supposed to bea coordinated and systematic process for carrying out allactivities related to providing and maintaining pavementsOn the other hand a PMMS should be able to predict thepavement condition and the cost associated with its MampRover a given time frame and also to aid in the planning andprogramming of the associatedMampRworks In implementingPMMS multicriteria priority ranking and analysis can beused to rank and select pavement sections due for mainte-nance in the order of urgency PMMS is considered to be atimely cost-beneficial and preventive MampR approach in themaintenance as compared to the traditional reactive MampRapproach

Pavement Maintenance Prioritization Using MulticriteriaDecision Approach The main multicriteria decision makingapproach is the Analytic Hierarchy Process (AHP) which was

Hindawi Publishing CorporationAdvances in Civil EngineeringVolume 2015 Article ID 140189 17 pageshttpdxdoiorg1011552015140189

2 Advances in Civil Engineering

PMMS Pavement maintenance

Pavement construction

Pavement design

Pavement planning

Pavement evaluation

Pavement research

Bridges Side walk Traffic signs

PMS

MampR

Road furniture

Figure 1 Schematic structure of a typical pavement management system (PMS) and pavement maintenance and management system(PMMS)

introduced by Saaty in the 1970s [4 5] Saaty developed AHPto primarily meet the complexities and challenges of decisionsituations that are brought out by multiple and conflictingcriteria as a multicriteria decision making (MCDM) toolAHP aids decisionmakers in determining the best criteria outof multiple sets of criteria based on crisp or exact numericalvalues

On road pavement maintenance priority ranking andanalysis AHP has been widely used (eg [6 7]) Howeverdue to the fact that in most practical situations the humanpreference is marred by uncertainty decision makers wouldfind it difficult to explicitly assign exact numerical valuesto the comparison judgments [8] Therefore the decisionmaker would theoretically find it very difficult to express thestrength of his preferences and confidence in terms of theAHP in pairwise comparison judgments As such AHP hasbeen argued to be ineffective when employed to ambiguousor vaguely represented real-life problems that consist ofuncertainty and subjectivity [9]

In decision making processes uncertainty imprecisionand subjectivity can be handled by means of probabilitytheory and or fuzzy set theory (FST) [10] While probabilityfocuses on the stochasticity of the decision making processFST tends to formalize the subjective and imprecise natureof human behavior by representing and quantifying vagueinformation through a membership grade function [10]As such probabilistic theory is not adequately suited forsubjectivity and imprecision in the human decision makingprocess [11ndash14]

The advantage of fuzzy based pairwise comparison isthat it allows decision makers to be more flexible in theirjudgments This is attained through the different degreesof fuzzification Furthermore if there is need for consider-ation of the attitude toward risk FTS has the possibility ofoverlapping preferences of criteria in case the expert is notconfident about the degree of importance within a set ofdecisions and there is the provision for interval decision asexpressed by a fuzzy membership function [15] FST can alsobe considered useful in decision problems where the degreesof uncertainty are expected to increase or change in time

for example in pavement failure and deterioration wheredifferent conditions are expected to change with time butthere is no predictive information on the future state

In order to accommodate uncertainty in expertsrsquo heuristicand experiential judgments Shah et al [3] used the rankingof road maintenance factors based on subjective rating Andto take care of subjectivity in judgment fuzzy pairwisecomparison deduction technique can be integratedwithAHP[3 16 17] Used independently fuzzy AHP results are directlyranked according to the normalized weights However inreal life decision decision makersrsquo degrees of confidence andattitudes to risks should be taken into consideration

Fuzzy Technique for Order Preference by Ideal Situation(TOPSIS) technique operates on the basis that the most pre-ferred decision alternative should not only have the shortestdistance from a positive ideal solution (PIS) but also havethe farthest distance from the negative ideal solution (NIS)hence its capability and efficiency in handling uncertainty[18 19] However the use of EuclideanDistance as determinedfrom PIS and NIS in TOPSIS does not consider the corre-lation of attributes and that makes it difficult to derive theweights of the decision attributes while keeping the judgmentconsistency [20] Thus the integration fuzzy TOPSIS withAHP is considered in this study in addition to taking intoaccount the degree of confidence in decision making

In this study fuzzy approach allowing experts to uselinguistic variables is considered for prioritization by apply-ing and comparing the results from fuzzy AHP and fuzzyTOPSISThe classical AHP is utilized to determine theweightvector of road maintenance factors with respect to the setobjectives In principle therefore the two approaches differprimarily in the way the fuzzy ratings are aggregated andnormalized but do impact on the data collection procedure

First a methodological overview and approach for fuzzyAHP and fuzzy TOPSIS for the formulation and automationof cost-effective PMMS for consistent and reliable prior-itization of MampR of road pavements in urban areas arepresented In the implementation a case study in EldoretTown in Kenya is used For thematic display of the roadnetwork a graphical user interface was designed in GIS and

Advances in Civil Engineering 3

Pavement distress data collection

Surface condition rating (SCR)

Pavement smoothness and roughness index

(SRI)

Pavement quality index (PQI)

Pavement maintenance objectives or treatments and thematic display system

Analytic hierarchy process (AHP) decision making matrix (X)

Fuzzy AHP andfuzzy TOPSIS

Pavement maintenance function ranking for prioritization based on pairwise analysis of

maintenance functions

Comparative analysis of performance index and ranking index

Pairwise maintenance objective weighting

(W)

Structuring hierarchy for maintenance objective and pairwise comparison

Fuzzy performance matrix (Z)

Defuzzification of priorities

Calculate fuzzy weights

Consistency check analysis

Manual-based condition rating and prioritization

Fuzzy AHPmdashobtain

Figure 2 Schematic framework for road pavement prioritization using fuzzy AHP and fuzzy TOPSIS

SQL database management systems In summary Figure 2presents the schematic framework for the methodologicalapproach in this study

The rest of the paper is organized as follows Section 2is on the case study pavement distress data collection cat-aloging and display Section 3 presents the methodologicaloverview and approach based on fuzzy AHP and fuzzyTOPSIS Section 4 presents the results of the case study andSection 5 presents the analysis and discussions of the resultsThe study conclusions and recommendations are presentedin Section 6

2 Case Study Pavement Distress Catalogueand Display

There are two main approaches for the collection of pave-ment distress data manual (visual inspection) distress datacollection and automated distress data collection [21] Forcost-effective and simplified pavement condition surveysthis study adopted empirically manual-based inspectionapproach to identify the pavement failures or distresses GPSwas used to obtain the chainages of the observed pavementfailures and to locate the associated pavement distresses


Pavement spatial information data collection

(pavement distress database)

Pavement inventory and digital image capturing

Pavement condition and position mapping

Database and thematic display using SQL

Statistical data representation and analysis

Graphical query interface

Distress reports display

Views Tables Charts Layouts

Pavement condition data analysis formaintenance prioritization using

fuzzy AHP and fuzzy TOPSIS

Figure 3 Proposed framework for pavement inventory and condition survey thematic display system

Location of Nandi road in Eldoret Town

0 02 04 08 12 16

(km) N

E

S

W

Nakuru-Eldoret roadNandi road

Figure 4 Study road and the adjoining roads digitized and georef-erenced from Google Maps image and GPS field observations

A summary of the structure for the pavement distresscatalogue and display system is presented in Figure 3 Theresult of this stage of mapping is presented in Figure 4 for thecase study of Nandi road in Eldoret Town (Kenya)

21 Pavement Distress Inventorying and Failure Index Sincethe collection of detailed pavement condition data is very

costly and time-consuming innovative approaches for rapiddata collection are in increasing demand among highwayagencies with limited PMS budgets [22] For the case studyvisual based empirical inspection and rating (ECR) fordistresses data collection was adopted for the 3 km Nandiroad with observations made at 300m segments For eachinspected segment of the road a digital image of the observeddistresses was also captured for thematic display

In order to determine the degree of distress failure twoapproaches are used One is a surface condition rating (SCR)to define the failure criteria for cracking and pothole baseddistresses According to the proposed SCR a rating scale of0ndash3 was adopted with a new road surface (no pothole nocracking) having an SCR of 3 As the amount and severity ofthe defect increase the SCR also drops That implies that lowcracking has an SCR of 3 while medium to severe crackingranges from 2 to 0 In terms of the defect extent defined bythe depth area andor length an SCR of 3 implies negligibledefects while SCR index values of 2ndash0 imply wide or longdefects that require repairs

The second component of pavement failure is the pave-ment surface ride quality This was characterized by patchingand raveling distresses indicators and expressed in terms ofthe degree of smoothness or roughness index (SRI) The SRIis also ranked between 3 and 0 such that a new roadpavementwould have an SRI of 3 SRI indices of between 2 and 1 implythat the road has deteriorated to the extent where motoristsfeel that it is uncomfortable driving on and therefore needsrehabilitation An SRI of 0 then means that there is completesurface failure requiring major rehabilitation as is character-ized by continuous cracking potholes patching and ravelingdistresses The pavement distresses that make up the generalpavement condition are determined by the expert judges


comprising of pavement engineers and road inspectors fromthe road management department

From the expertsrsquo judgments and analyses it was deducedthat the overall road pavement quality index (PQI) indicatoris defined by the geometricmean of SCR and SRI as expressedin (1) In (1) PQI values range from 3 to 0 with a PQI valueof between 2 and 0 implying that the pavement is subject tomaintenance andor rehabilitation

PQI = radicSCR lowast SRI (1)

In the implementation it is recommended that PQI indicesshould not be rounded off that is a PQI of radic1 lowast 3 = radic3 =

1732 is not equivalent to 2 This precaution is taken in orderto avoid minor repair maintenances at any given time inthe pavement life-span for economic reasons at the expenseof more immediate and larger MampR cases From the PQIthe road pavement maintenance objectives and functions canthen be derived

A summary of the observed distress results for the 3 kmroad is presented in Table 1 The results in Table 1 showthat the distresses were mainly characterized by crackingpotholes patching and raveling The results in Table 1 willbe subjected to pairwise comparison and prioritization bythe pavement management experts in order to determine thepriority areas for MampR activities Figure 5 characteristicallyshows some of the functional and structural failures that areobserved on the case study road as summarized in Table 1

3 Methodology

31 AHP for Decision Prioritization AHP is often usedto guide decision makers coping with multicriteria deci-sions involving multiattribute situations [5 23ndash25] Decisionjudgments as articulated by pairwise comparisons are thefundamental inputs for facilitating the AHP procedure Everypairwise comparison results in a numerical value 119886

119894119895repre-

senting the ratio between the weights of the two decisioncriteria 119894 and 119895 The Saaty preference scale is used to assignnumerical values to different levels of preferences As astandard the Saaty scale used for AHP ranges from 1 to 9and reflects the importance of one factor over another asrepresented in Table 2

Supposing that 119862 = 119862119895| 119895 = 1 2 119899 is the set of

criteria then the evaluationmatrix can be obtained in whichevery element 119886

119894119895(119894 119895 = 1 2 119899) represents the relative

weights of the criteria illustrated

119860 =

[[[[[[

[

11988611 11988612 sdot sdot sdot 1198861119899

11988621 11988622 sdot sdot sdot 1198862119899

1198861198991 1198861198992 sdot sdot sdot 119886

119899119899

]]]]]]

]

(2)

In (2) 119899 is the number of criteria in a decision processsuch that 119860 is the judgment which contains the pairwisecomparison value 119886

119894119895for all 119894 119895 isin 1 2 119899

For multiple decision makers or experts as is often thecase if ℎ is the number of decision makers and 119886

119896

119894119895is the

Table 1 Road condition survey data showing pavement segmentchainage and the observed distresses as derived from the PQIcalculations

Segment or chainage (m) Observed distresses

0ndash300(i) Potholes(ii) Longitudinal cracks(iii) Transverse cracks(iv) Alligator cracks

300ndash600(i) Longitudinal cracks(ii) Transverse cracks(iii) Block cracking

600ndash900

(i) Potholes(ii) Longitudinal cracks(iii) Transverse cracks(iv) Alligator cracks(v) Patching

900ndash1 200(i) Potholes(ii) Longitudinal cracks(iii) Alligator cracks

1 200ndash1 500(i) Potholes(ii) Longitudinal cracks(iii) Edge cracking(iv) Raveling

1 500ndash1 800(i) Potholes(ii) Longitudinal cracks(iii) Transverse cracks(iv) Block cracking

1 800ndash2 100(i) Potholes(ii) Longitudinal cracks(iii) Alligator cracks



2 700ndash3 000

(i) Potholes(ii) Longitudinal cracks(iii) Transverse cracks(iv) Alligator cracks(v) Block cracking(vi) Raveling

pairwise comparison value of criteria 119894 and 119895 given by decisionmaker 119896 where 119896 = 1 2 ℎ then by using geometric meanof the 119886119896

119894119895conducted by each decisionmaker a new compound

judgment matrix is derived with the corresponding elementsdetermined as follows

119886119894119895= (119886

1119894119895lowast 119886

2119894119895lowast sdot sdot sdot 119886

119896


ℎ

119894119895)1ℎ

= (

ℎ

prod

119896=1

119886119896

119894119895)

1ℎ

(3)

The basic procedure for AHP approach as represented by themean of normalized values method can be summarized inthe following steps according to Saaty [26] (i) normalizationof each column to get a new judgment matrix (119860

1015840) (ii)

summing up of each row of normalized judgment matrix


Table 2 The nine-point Saaty scale of relative importance [4]

Intensity of importance Definition Explanation1 Equal importance Two activities contribute equally to the objective

3 Weak importance of oneover the other

Experience and judgment slightly favour one over theother

5 Essential or strongimportance

An activity is strongly favoured and its dominance isdemonstrated in practice

7 Demonstrated importance The evidence favouring over another is of highestpossible order of affirmation

9 Absolute importance When compromise is needed2 4 6 8 Intermediate values

(a) Transverse cracking (b) Alligator (fatigue) cracking (c) Edge cracking

(d) Pothole (e) Raveling-microtextural surface deformations

Rutting

(f) Rutting and block cracking

(g) Patching

Figure 5 Photographs of typically observed road pavement distresses

(1198601015840) to get weight vector (119881) and (iii) finally defining the

final normalization weight vector (119882) Detailed and stepwiseimplementation of the AHP techniques can be found inOuma and Tateishi [25]

According to the relative importance in Table 2 a deci-sionmaker who for example assigns a value of 3 to a pairwisecomparison implies that the judgment slightly favours one

alternative over the other However because of the subjectivenature in linguistic decisions (eg very high high moderatelow and very low) such an assessment cannot be accurateFurthermore when the decision makerrsquos judgments areuncertain determining such precise Saatyrsquos static nine-pointscale values may be very difficult This means that the staticcrisp values may lack the ability to capture the decision


0

1

Am1 m2 m3

120583A

Ar(y) Ar(y)

(a)

1

V(A

2geA

1)

M2 M1

l2 m2 l1 d u2 m1 u1

(b)

Figure 6 (a) A triangular fuzzy number119872 and (b) the intersection between1198721 and1198722 in extent fuzzy analysis

makersrsquo ambiguous andor vague preferencesThe logical wayto overcome this limitation is to define the comparison ratiosin terms of fuzzy numbers

32 Fuzzy SetsTheory and Fuzzy AHP In contrast to classicalset theory FST allows for the assessment of the membershipof elements with respect to a set represented by 120583 = [0 1][10] The fuzzy AHP is an extension of AHP technique formulticriteria decisionmaking in pairwise based comparisonsthat deals with qualitative and imprecise real-world decisionsproblems

In essence fuzzyAHP is a synthetic extension of the classi-cal AHPmethodwhen the fuzziness of the decisionmakerrsquos isconsidered Fuzzy AHP is comprised of the following steps inimplementation (i) structuring of the levels of hierarchy fordecision making (ii) prioritization based on fuzzy pairwisecomparisons (iii) checking for consistency of the preferencejudgments by the experts (iv) synthesis of pairwise prioritiesand (v) defuzzification of the determined priorities accordingto Chen and Hsieh [27] Defuzzification is necessary becausethe fuzzy arithmetic means are not crisp values and hencecannot directly be ranked Defuzzification thus refers to thefuzzy ranking method that is employed so as to obtain thedesired nonfuzzy or crisp values [28]

A fuzzy AHP decision problem consists of a number ofalternatives [119872

119894(119894 = 1 2 119898)] a set of evaluation criteria

[119862119895(119895 = 1 2 119899)] a linguistic judgment (119903

119894119895) representing

the relative importance of each pair of criteria and a weight-ing vector [119882 = (1199081 1199082 119908119899)] Like the classical AHPfuzzy AHP also has a judgment matrix However the extentfuzzy approach uses the triangle fuzzy numbers (TFNs)instead of a constant pairwise comparison value [29] Theextent analysis based fuzzy AHP depends on the degree ofpossibilities of each criterion used in the decision processTFNs for the linguistic variables from the judgments areplaced according to the responses and for a particular level onthe decision hierarchy from which the pairwise comparisonmatrix is constructed [30 31]

According to Kaufmann and Gupta [32] a fuzzy number119865 is a triangular fuzzy number if its membership function120583119865(119909) R rarr [0 1] is defined according to (4) and is

depicted in Figure 6 As in (4) the comparison ratios between

the success factors 119894 and 119895 are characterized with TFNwhich describes the judgment about 119886

119894119895and are denoted

by 119886119894119895 Hence it is possible to describe some degree of

vague or ambiguous human perception and decision inpairwise comparisons In Figure 6(a) a TFN is denoted byeither (11989811198982 11989821198983) or (1198981 1198982 1198983) For a fuzzy eventthe parameters 1198981 1198982 and 1198983 in Figure 6(a) respectivelydenote the smallest possible value the most promising valueand the largest possible value Each TFN has linear represen-tations on its left and right sides such that its membershipfunction can generally be defined as follows

120583119860(119909) =

(119909 minus119897

119898minus 119897) 119897 le 119909 le 119898

(119906 minus119909

119906minus 119898) 119898 le 119909 le 119906

0 otherwise

(4)

where 119897 (= 1198981) and 119906 (= 119898

3) respectively represent the

lower and upper bounds of the fuzzy number 119860 while 119898 (=

1198982) is themedian value as shown in Figure 6(a) Thus a TFN

is generally denoted by 119860 = (119897 119898 119906)As shown in Figure 6(a) a fuzzy number can be given by

its corresponding left and right representation of each degreeof membership defined by

119860 = (119860119897(119910)

119860119903(119910)

)

= (1198981 + (1198982 minus1198981) 1199101198983 + (1198982 minus1198983) 119910)

forall119910 isin [0 1]

(5)

where 119897(119910) and 119903(119910) denote the left side representation andthe right side representation of a fuzzy number respectivelyMatrix 119860 represents an (119899 times 119899) judgment matrix containingTFNs (119886

119894119895) for all 119894 119895 isin 1 2 119899 as expressed in the

following

119860 = (119886119894119895) =

[[[[[[

[

(1 1 1) 11988612 sdot sdot sdot 1198861119899

11988621 (1 1 1) sdot sdot sdot 1198862119899

1198861198991 119886

1198992 sdot sdot sdot (1 1 1)

]]]]]]

]

(6)


Table 3 (a) Fuzzy linguistic variables and corresponding fuzzy numbers (b) Fuzzy number memberships of pairwise comparisons [8]

(a)

Linguistic variable Fuzzy number Membership function Definition

Equally important 1 (1 1 2)Practical knowledge and experience implythat factor 119894 is equally important whencompared to factor 119895

Moderately important 3 (2 3 4)Practical knowledge and experience implythat factor 119894 is moderately more importantwhen compared to factor 119895

More important 5 (4 5 6)Practical knowledge and experience implythat factor 119894 is more important whencompared to factor 119895

Strongly important 7 (6 7 8)Practical knowledge and experience implythat factor 119894 is strongly important whencompared to factor 119895

Extremely important 9 (8 9 9)Practical knowledge and experience implythat factor 119894 is extremely important whencompared to factor 119895 and totally outweighsit

(b)

119886 Fuzzy number 119886 Fuzzy number1 (1 1 2) 050 (033 05 1)2 (1 2 3) 033 (025 033 05)3 (2 3 4) 025 (02 025 033)4 (3 4 5) 020 (017 02 025)5 (4 5 6) 017 (014 017 02)6 (5 6 7) 014 (013 014 017)7 (6 7 8) 013 (011 013 014)8 (7 8 9) 011 (011 011 013)9 (8 9 9) Diagonal elements (1 1 1)

In general 119886119894119895= (119897119894119895 119898119894119895 119906119894119895) with 119897

119894119895being the lower limit 119906

119894119895

the upper limit and119898119894119895the most likely value such that119898

119894119895=

radic119897119894119895lowast 119906119894119895 Assume that 1198601 and 1198602 are two triangular fuzzy

numberswith1198601 = (1198971 1198981 1199061) and1198602 = (1198972 1198982 1199062) Some ofthe fuzzy functional operators (additive multiplicative andinverse) are represented in the following

1198601 oplus1198602 = (1198971 + 1198972 1198981 +1198982 1199061 +1199062) (7)

1198601 otimes1198602 = (11989711198972 11989811198982 11990611199062) (8)

119860minus11 = (

11199061

11198981

11198971) (9)

The outcome of each set of pairwise comparisons is expressedas a fuzzy positive reciprocal (9) matrix 119860 = 119886

119894119895 such

that if 119886119894119895

= 1 then 119886119894119895

= 1119886119895119894for all 119894 119895 le 119899 where 119899

denotes the number of alternatives being compared withinone set of pairwise comparisons 119886

119894119895denotes the importance

of alternative 119894 over alternative 119895 119886119895119894denotes the importance

of alternative 119895 over alternative 119894 and 119886119894119895= (119897119894119895 119898119894119895 119906119894119895)

The definitions of TFN values in Table 3 are used to facil-itate the use of pairwise comparisons in fuzzy based decisionprocesses TFN (119886) in Table 3 means that the decision maker

thinks the importance ratio of two alternatives is about 119886 InTable 3(a) particular linguistic assessment terms called fuzzylinguistic variables are introduced to represent the underlyingfuzzy numbers employed for factor evaluations For thisstudy five fuzzy linguistic variables are used to capture thesubjective judgments about the relative importance of a factorversus another The linguistic variables are summarized inTable 3(a) as equally important moderately important moreimportant strongly important and extremely important InTables 3(a) and 3(b) a summary of the fuzzy linguisticvariable set with lower most likely and upper values ofunderlying TFN and their definitions are given

After the decision criteria have been determined asdepicted in Figure 6(b) a judgment approach for determin-ing the importance levels of these criteria is established Toevaluate the decision judgments the decision makers selectthe related linguistic variables then for calculations they areconverted into the TFN and generalized for such analysis aspresented in Table 3 The fundamental step in fuzzy AHPmethodology is the prioritization procedure whereby theprioritization problem is defined as deriving the unknownpriority vector from the judgment set119860 The basic procedureof the fuzzy AHP can be summarized in the following fourmain steps [33]


Step 1 (developing and structuring of the decision hierarchy)This first step comprises the restructuring the complexdecision making problem into a hierarchical structure Thederived structural framework is significant in understandingthe interactions amongst the elements involved in eachdecision level and aids the decision makers in exploringthe impacts of the different decision components on theevaluation system

Step 2 (building of the fuzzy pairwise comparison matrices)First the relative importance of the criteria is determinedthrough pairwise comparison of the decision criteria Afterexpert evaluations the relative importance is transformedinto triangular fuzzy numbers [25] By considering a pri-oritization problem at a decision level with 119899 elementseach set of comparisons for a given level requires 119899(119899 minus

1)2 judgments which are used to construct a positivefuzzy reciprocal comparison matrix 119860 = 119886

119894119895 as given in

(6)

Step 3 (consistency check and fuzzy weights priorities deriva-tion) This step checks for decision consistency and deter-mines the priorities from the pairwise comparison matrices[25] A fuzzy comparison matrix 119860 = 119886

119894119895 is consistent if

119886119894119896

otimes 119886119896119895

asymp 119886119894119895 where 119894 119895 119896 = 1 2 119899 [34] After the

consistency check the fuzzy priorities119908119894are calculated from

which the priority vectors (1199081 1199082 119908119899)119879 are obtained

from the comparison matrix by applying a prioritizationranking approach [31]

Step 4 (defuzzificationmdashconversion of the fuzzy weightsto crisp weights) Defuzzification can be solved using thegraded mean integration representation (GMIR) method byChen and Hsieh [27] and Hsieh et al [35]

119903119894= (1198861198941 otimes sdot sdot sdot otimes 119886

119894119895otimes sdot sdot sdot otimes 119886

119894119899)1119899

119908119894= 119903119894otimes [1199031 oplus sdot sdot sdot oplus 119903

119894oplus sdot sdot sdot oplus 119903

119899]minus1

(10)

where 119886119894119895

is fuzzy comparison value of dimension 119894 tocriterion 119895 119903

119895is a geometric mean of fuzzy comparison value

of criterion 119894 to each criterion and 119908119894is the fuzzy weight of

the 119894th criterion which can be indicted by a triangular fuzzynumber 119908

119894= (119897119908119894 119898119908119894 119906119908119894) [35]

Step 5 (calculation andnormalization of theweight vector andalternatives ranking) The crisp values are normalized in thisstage This final step aggregates the local priorities obtainedat the different levels of the decision structure hierarchy intothe composite priorities for the alternatives according to theweighted sum 119860

119894= sum119899

119895=1 119908119895119886119894119895 where 119908119895is the weight of

criterion 119895 The higher is the value of 119860119894 the more preferred

is the alternative

33 Fuzzy TOPSIS The fundamental principle of the TOPSISmethod is that the chosen alternative should have the shortestdistance from the positive ideal solution (PIS) and the farthestdistance from the negative ideal solution (NIS) If in aMCDM

problem decision process there are 119899 criteria (1198621 1198622 119862119899)amongst 119898 alternatives (1198601 1198602 119860119898) then accordingTOPSIS principle the performance of the alternative 119894 atthe criterion 119895 is such that the best alternative should havethe shortest distance from the PIS and the farthest distancefrom the NIS The TOPSIS considers the PIS and NIS asthe reference points and does not take into considerationthe relative importance of the distances from these points[36]

Fuzzy TOPSIS where TOPSIS refers to Technique forOrder Preference by Similarity to Ideal Situation is a mul-ticriteria decision evaluation method for selected criteriaThe principle of TOPSIS approach is that an alternative thatis nearest to the Fuzzy Positive Ideal Solution (FPIS) andfarthest from the Fuzzy Negative Ideal Solution (FNIS) ischosen as optimal [37 38]

The following steps give a summary of the fuzzy TOPSISmulticriteria decision making method [36 39]

Step 1 (assignment of ratings to the criteria and the alter-natives) If there are 119869 possible candidates denoted by 119860 =

1198601 1198602 119860119895 to be evaluated against 119899 criteria 119862 = 11986211198622 119862119895 and the criteria weights are denoted by 119908

119894119894 =

1 2 119898 then the performance ratings of each decisionmaker 119863

119896119896 = 1 2 119870 for each alternative 119860

119895119895 = 1

2 119899 with respect to criteria 119862119894119894 = 1 2 119898 are

denoted by 119896= 119909119894119895119896

(119894 = 1 2 119898 119895 = 1 2 119899 119896 = 12 119870) with the membership function 120583

119896(119909)

Step 2 (compute and aggregate the fuzzy ratings for thecriteria and the alternatives) If the fuzzy ratings of alldecision makers are described as triangular fuzzy number119896= (119886119896 119887119896 119888119896) then the aggregated fuzzy rating is given by

= (119886 119887 119888) where 119896 = 1 2 119870 where

119886 = min119896

119886119896

119887 =1119870

119870

sum

119896=1119887119896

119888 = max119896

119888119896

(11)

If the fuzzy rating and importance weight of the 119896th decisionmaker are119909

119894119895119896= (119886119894119895119896 119887119894119895119896 119888119894119895119896) and the correspondingweights

are119908119894119895119896

= (1199081198941119896

1199081198942119896

1199081198943119896

) then the aggregated fuzzy ratings119909119894119895of the alternatives with respect to each criterion are given

by 119909119894119895= (119886119894119895 119887119894119895 119888119894119895) where

119886119894119895= min119896

119886119894119895119896

119887119894119895=

1119870

119870

sum

119896=1119887119894119895119896

119888119894119895= max119896

119888119894119895119896

(12)


The aggregated fuzzy weights 119908119894119895of each criterion are then

calculated by 119908119895= (1199081198951 1199081198952 1199081198953) where

1199081198951 = min

119896

1199081198951198961

1199081198952 =

1119870

119870

sum

119896=11199081198951198962

1199081198953 = max

119896

1199081198951198963

(13)

Step 3 (compute the fuzzy decision matrix) The fuzzy per-formancedecision matrix for the alternatives (119863) and thecriteria () is constructed as follows This is followed bythe choice of the appropriate linguistic variables for thealternatives with respect to criteria

119863 =

1198621 1198622 sdot sdot sdot 119862119899

1198601

1198602

119860119898

[[[[[

[

11990911

11990921

sdot sdot sdot

1199091198981

11990912

11990922

sdot sdot sdot

1199091198981

sdot sdot sdot

sdot sdot sdot

sdot sdot sdot

sdot sdot sdot

1199091119899

11990921

sdot sdot sdot

119909119898119899

]]]]]

]

(14)

where 119909119894119895= (1119870)(119909


119896


119870

119894119895) with 119909

119896

119894119895being

the performance rating of alternative119860119894with respect to 119862

119895as

evaluated by the 119896th decision maker 119909119896119894119895

= (119897119896

119894119895 119898119896

119894119895 119906119896

119894119895) and

= (1199081 1199082 119908119899) [40]

Step 4 (normalize the fuzzy decision matrix) The raw dataare normalized using linear scale transformation in order tobring the various criteria scales into a comparable scale Thenormalized fuzzy decision matrix is given by

= [119903119894119895]119898times119899

119894 = 1 2 119898 119895 = 1 2 119899 (15)

where 119903119894119895= (119886119894119895119888lowast

119895 119887119894119895119888lowast

119895 119888119894119895119888lowast

119895) and 119888

lowast

119895= max

119894119888119894119895are called

the benefit criteria and 119903119894119895= (119886minus

119895119888lowast

119895 119886minus

119895119887lowast

119895 119886minus

119895119886lowast

119895) and 119886

minus

119895=

min119894119886119894119895are called the cost criteria

Step 5 (compute the weighted normalized matrix) Theweighted normalized matrix () for criteria is computed bymultiplying the weights (119908

119895) of evaluation criteria with the

normalized fuzzy decision matrix 119903119894119895

= [V119894119895]119898times119899

= [119903119894119895 (sdot) 119908119894119895]

119894 = 1 2 119898 119895 = 1 2 119899(16)

Step 6 (compute the fuzzy positive ideal solution (FPIS)and fuzzy negative ideal solution (FNIS)) The FPIS andFNIS of the alternatives are computed as follows From theweighted normalized fuzzy-decision matrix the elements V

119894119895

are normalized positive TFNswithin the closed interval [0 1]Then FPIS (119860+) and FNIS (119860minus) are calculated [41]

119860+= (V+1 V

+

2 V+

119899)

where V+119895= max119894

V1198941198953 119894 = 1 2 119898 119895 = 1 2 119899

119860minus= (Vminus1 V

minus

2 Vminus

119899)

where Vminus119895= max119894

V1198941198951 119894 = 1 2 119898 119895 = 1 2 119899

(17)

Step 7 (compute the distance of each alternative from FPISand FNIS) Thedistance (119889+

119894 119889minus

119894) of eachweighted alternative

119894 = 1 2 119898 from the FPIS and the FNIS is computed asfollows using the area compensation method

119889+

119894=

119899

sum

119895=1119889V (V119894119895 V

+

119895) = [

[

13

119899

sum

119895=1(V119894119895minus V+119895)2]

]

12

119894 = 1 2 119898

119889minus

119894=

119899

sum

119895=1119889V (V119894119895 V

minus

119895) = [

[

13

119899

sum

119895=1(V119894119895minus Vminus119895)2]

]

12

119894 = 1 2 119898

(18)

where 119889V(119886 ) is the distance measurement between twofuzzy numbers 119886 and

Step 8 (compute the closeness coefficient (CC119894) of each

alternative) The closeness coefficient (CC119894) or the degree of

relative gaps that represents the distances to the fuzzy positiveideal solution (119860

lowast) and the fuzzy negative ideal solution (119860

minus)

is computed The closeness coefficient of each alternative iscalculated as

CC119894=

119889minus

119894

119889minus

119894+ 119889+

119894

= (1minus119889+

119894

119889minus

119894+ 119889+

119894

)

for 119894 = 1 2 119898

(19)

where 119889minus119894(119889minus

119894+ 119889+

119894) is the fuzzy satisfaction degree in the 119894th

alternative and 119889+

119894(119889minus

119894+119889+

119894) is the fuzzy gap degree in the 119894th

alternative

Step 9 (ranking the alternatives) In the last step the differentalternatives are ranked according to the closeness coefficient(CC119894) in decreasing orderThe best alternative is closest to the

FPIS and farthest from the FNIS

4 Case Study Results and Analysis

41 GIS-SQL Database for Thematic Displays of PavementDistress Data Figure 7 shows the typical output of the resultsfor the GIS-SQL based graphical thematic display of theroad condition survey for the Nandi road distress betweensegments 2 100m and 2 400m The segment query results


Table 4 Case study maintenance functions for the observed distresses

Distress treatment (maintenance function) forobserved distress Fog seal Micro

surfacingSlurryseal

Capeseal Chip seal Thin HMA

overlay Resurfacing

Rutting times times

Alligator and block cracking times times times times times times

Longitudinal and transverse cracking times times times times

Pothole times times times

Raveling times times times times times

Resurfacing times times times

2+400

2+100

Figure 7 An SQL based thematic graphical display of roadpavement distress at specified segments

display the following information regarding the segmentthe chainage of the road segment surveyed the distressesobserved within the segment and the distress images Suchpavement condition data representation can easily be lever-aged into a web access platform so as to be easily accessibleto the different levels of urban road maintenance and man-agement

A summary statistic on the frequency of occurrence ofdistress types is also generated for the entire surveyed roadpavement as presented in Figure 8 Results in Figure 8 showthe most and least frequent distresses on the road as longitu-dinal cracks and patching respectively A plot of the degreeof distress that is low medium or high can also be derivedfrom the empirically observed and categorized severity ofdistresses though such linguistic information is captured inthe distress survey by the condition assessment experts

42 Case Study Road Maintenance Treatments From theobserved distresses presented in Table 1 and in Figure 5 thepossible maintenance treatments and functions are deter-mined with the results presented in Table 4 From thecondition survey results it was observed that there wereseven main pavement distresses or maintenance functionsalong the 3 km road From the results in Table 4 it was notedthat if the distresses identified in the pavement conditionsurvey are related to structural deficiencies then the road

0

2

4

6

8

10

12

Poth

oles

Long

itudi

nal

crac

ks

Tran

sver

secr

acks

Alli

gato

rcr

acki

ng

crac

king

Bloc

k

Rave

ling

Patc

hing

Occ

urre

nce o

f dist

ress

Observed distress (date 04122013)

Eldoret City Nandi road condition inspectionthematic display tabular summary

(0+000

ndash3+000

km)

Figure 8 Summary of the distresses report of for the case study

section is most likely not to be a candidate for a preventivebasic maintenance treatment but rather for rehabilitation

The results in Table 4 are summarized as follows (i) fogseal it is an application of diluted emulsion (normally 1 to1) to enrich the pavement surface and hinder raveling andoxidation and is considered as a temporary application (ii)crack sealing this treatment is used to prevent water anddebris from entering cracks in the pavement the treatmentmight include routing to clean the entire crack and to createa reservoir to hold the sealant (iii) chip seal this treatmentis used to waterproof the surface seal small cracks andimprove friction although it is typically used on low volumeroads and streets it can also be used on high volume roadsand highways (iv) thin cold mix seals these treatmentsinclude slurry seals cape seals and micro surfacing whichare used on all types of facilities to fill cracks improvefriction and improve ride quality (v) Thin Hot Mix Asphalt(HMA)overlays these include dense- open- and gap-gradedmixes (as well as surface recycling) that are used to improveride quality provide surface drainage and friction and cor-rect surface irregularities Thin HMA overlays are generally37mm in thickness and (vi) resurfacing resurfacing of a roadpavement in totality or section thereof is normally carried outin order to add strength to the asphalt layer and to prolong itslife and or to correct a specific section or the entire surfaceprofile and in order to improve on the riding quality andsurface water drainage


Table 5 Round 1 of decision based on importance of allocation or weighting

Road pavement maintenance objectives Pavement expert (engineerinspectorplanner) Maintenance relative weights1 2 3 4 5 6 7 8 9 10

Road safety 35 45 45 30 40 45 35 50 30 35 039Pavement surface preservation 40 30 20 40 30 25 30 20 30 40 031Road operational status and standards 15 15 20 20 15 20 25 20 20 15 019Road aesthetics 10 10 15 10 15 10 10 10 10 10 011

Table 6 Round 2 of judgment based on incremental linear ranking with 10 as the lowest importance

Road pavement maintenance objectives Pavement expert (engineerinspectorplanner) Maintenance relative weights basedon linear scale1 2 3 4 5 6 7 8 9 10


Table 7 Round 3 of decision according to crisp scale based ranking (with 1 being the least important and 5 the most important)

Road pavement maintenance objectives Pavement expert (engineerinspectorplanner) Maintenance relative weights basedon 1ndash5 crisp scale1 2 3 4 5 6 7 8 9 10


43 Maintenance Objectives Determination Weighting andAHP Hierarchical Structure To determine the maintenanceobjectives from the maintenance functions ten expertscomprising pavement engineers inspectors and transportplanners from Kenya Urban Roads Authority (KURA) gavetheir assessments and judgments on the maintenance objec-tives weighting for routine urban road maintenance Thiswas carried out by first selecting the maintenance objectiveswhere the experts were asked to nominate a number of main-tenance objectives based on the observed distresses (Table 4)From the expert evaluation results the top four maintenanceobjectives are adopted as the case study maintenance criteria

The selected road maintenance objectives were deter-mined respectively as road safety (RS) pavement surfacepreservation (PSR) road operational status and standards(ROS) or quality and road aesthetics (RA) (Table 5) Afterthe maintenance objectives are obtained the weights of theselected maintenance objectives are then determined

The same group of experts gave their estimates on thefour maintenance objectives weighting Each of the expertsassigned weights to the maintenance objectives in threerounds each round using a different approach comprising thefollowing elementsThe rationale of using the three rounds isto vary and objectively without biases determine the weightsbased on different ranking scales from percentages incre-mental decimals linear scale (10ndash50) and whole numberlinear scale (1ndash5)

(i) Round 1 in this round weighting is carried out interms of percentages and applied to eachmaintenanceobjective

(ii) Round 2 by using linear incremental scale with stepsof 025 the objective with the lowest importance isset at 10 and the one with the greatest importance isrecorded at 50 depending on the function

(iii) Round 3 on a linear scale of crisp values of 1ndash5(increasing at intervals of 1) the importance of theobjectives is ranked with 1 representing the leastimportant objective and 5 representing the mostimportant

Because of human objectivity reasoning and subjectivity atthe end of three rounds the results will vary based on theindividual decision makerrsquos perception of the criterion andin accordance with ranking scale used At the end the resultsare aggregated to minimize on subjectivity and to objectivelydetermine the overall weights Results for the three rankingsteps are presented in Tables 5ndash7 for the four maintenanceobjectives In the pavement expert columns 1 to 10 representthe ten decision experts

From the averaged AHP and fuzzy weights based eval-uation matrices represented respectively in Tables 8 and 9the final aggregated weighting vector was determined as119882 =

[037 031 022 010]119879 for the four maintenance objectivesand is presented in Table 10The results in Table 10 show thataccording to the experts road safety and surface conditionaccounted for 68 of themaintenance objectives preferenceswhile quality and aesthetics together contributed to 32 ofthe maintenance preferences

From the above results the final AHP hierarchical struc-ture of the maintenance prioritization levels is derived for


Table 8 Averaged AHP based evaluation matrix for the maintenance objectives

Road maintenance objectives Road safety Pavement surfacepreservation

Operational statusand standards Road aesthetics

Road safety 1 2 1 2Pavement surface preservation 05 1 05 075Operational status and standards 1 2 1 1Road aesthetics 05 133 1 1

Table 9 Equivalent fuzzy based evaluation matrix for maintenance objectives



Road safety (1 1 1) (133 2 4) (08 1 133) (1 2 3)Pavement surface preservation (033 05 075) (1 1 1) (025 05 1) (05 075 1)Operational status and standards (075 1 125) (1 2 3) (1 1 1) (05 1 125)Road aesthetics (033 05 1) (1 133 2) (08 1 133) (1 1 1)

Table 10 Average maintenance objectives weighting vector (119882) for the case study



Mean relative maintenanceobjective weights 037 031 022 010

the case study as presented in Figure 9 As already statedhierarchical structuring of a pavement maintenance prioriti-zation problem is an efficient way of dealing with the decisioncomplexity and is useful in identifying themajor componentsof the PMMS From Figure 9 it is seen that the structurefor the case study comprises three levels with the final levelbeing the overall goal and the other two levels the first lowerhierarchy is the maintenance functions and the secondhigher hierarchy is the maintenance objectives For realisticcost-benefit evaluation every MampR project should have itsown hierarchical structure

44 Multiattribute Analysis for Pairwise Comparisons ofMaintenance Objectives For the pairwise comparative eval-uation ten pavement engineers from KURA gave their judg-ments using pairwise comparisons of the four maintenanceobjectives All the ten engineers gave pairwise comparisonsto the seven maintenance functions with respect to the pre-determined four maintenance objectives The pairwise com-parisons are based onnine-point Saaty scale of relative impor-tance [26] as presented in Table 2 Using the fuzzification anddefuzzification rules as presented in Table 3 substitutes forthe crisp numbers and the fuzzy numbers are obtained

The optimal level of confidence is the degree of accuracywith which one is able to execute a given decision makingtask That is due to the subjective nature of the exercisean optimal level from experienced researchers is empiricallyconsidered to be neither too high nor too low and thereforea value above mean threshold of 60 is chosen On the otherhand the attitude towards risk is the effect of executing theparticular task within an errormargin For this case study theerrormargin for the decisionmakers is set amaximumof 50

chance and the errors are attributed to mistakes (gross) sys-tematic and random occurrencesThismeans that an optimalperformer should be able to execute the task with an accuracyof at least 60 and is liable to maximum error level of 50

By choosing an optimal level of confidence of (120572 = 60)and assuming a moderate attitude to risk of (120582 = 05) thefuzzy performance matrix (119885) is defuzzified under the opti-mal boundary conditions of [120572 = 06 120582 = 05] The matrixis normalized to satisfy the condition that the summationof all the seven maintenance functions under each criterionis 1 Therefore the crisp normalized performance matrix 119885

120582

120572

is obtained as below for the four pavement maintenanceobjectives and as determined by the ten experts

119885120582

120572=

RS PSR ROS RA100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816

(0199)(0464)sdot sdot sdot

(0170)


(0142)


(0161)


(0229)

100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816

(20)

The final maintenance functions ranking is then derived andthe results are presented in Tables 11 and 12 for fuzzy AHPand fuzzy TOPSIS The final performance index for eachmaintenance function is obtained by averaging the respectivepriorities as determined by each of the decision makers Itis observed that the results in Tables 11 and 12 are nearlythe same except for the rakings 5 and 6 Compared withthe manual-based evaluations and ranking which are basedon the set out guiding principles such distress type thedimensions (area length and depth) and significance ofthe road for the aggregation of individual ranking of each


Prioritization of road pavement

maintenance andrehabilitation

(MampR) functions

Road operational status and standards

(ROS)

Fog seal

Micro surfacing

Slurry seal

Cape seal

Chip seal

Thin HMA overlay

Resurfacing

Pavement surface preservation (PSR)

Road safety (RS)

Road aesthetics(RA)

Maintenance functionsMaintenance objectivesMampR goal

Figure 9 Three-level hierarchical structure of maintenance function prioritization process for the case study road

Table 11 Maintenance function ranking and performance rankingusing fuzzy AHP

Function number Maintenancefunction

Performanceindex Ranking index

1 Fog seal 0755 7

2 Microsurfacing 0798 6

3 Slurry seal 0870 34 Cape seal 0816 55 Chip seal 0852 4

6 Thin HMAoverlay 0883 1

7 Resurfacing 0879 2

distress and scoring the fuzzyTOPSIS results inTable 12werefound to be consistent with the prioritization experiences inpractice The top three maintenance functions (Thin HMAoverlay resurfacing and slurry seal) are all pavement relatedfunctions and are related to the pavement deficiencies andhave more direct impacts on the road pavement functions

5 Comparison of Fuzzy AHP and FuzzyTOPSIS Results

To compare variance in the decisions the fuzzy AHP andfuzzy TOPSIS were plotted on the same scale by rescaling theperformance indices of all the seven maintenance functionsto the same scale such that the normalized sum equals 1Figure 10 presents the results of the comparative ranking

indices The results in Figure 10 show that the fuzzy AHPtends to overestimate the ranking process as compared tothe fuzzy TOPSIS and the manual-based decision validationprocedure The results in Figure 10 show that the fuzzyTOPSIS results are quite close to manual-based approachwhich implies that the TOPSIS approach ismuchmore able tocapture the user degree of confidence Nonetheless differentcase studies can be carried out in order to generalize theeffectiveness of two fuzzy based prioritization techniquesespecially in different geographical regions

There are however similarities and differences in therankings as obtained from the two prioritization techniquesas seen in Figure 10 For example the top three maintenancefunctions are the same and only in the bottom three isthere a slight difference The results also show that thereis consistency in the fuzzy TOPSIS ranking process ascompared to the variability in ranking values in fuzzy AHP

Although fuzzy AHP and fuzzy TOPSIS have the sameobjective of prioritizing the maintenance objectives andfunctions throughMCDMprinciples they have fundamentaldifferences According to fuzzy AHP pairwise comparisonsby decision makers are made for the criteria and alterna-tives under each criterion The resulting comparisons areintegrated and decision makersrsquo pairwise comparison valuesare transformed into triangular fuzzy numbers The priorityweights of the criteria and alternatives are then derivedAccording to the combination of the priority weights ofcriteria and alternatives the best alternative is determined

In fuzzy TOPSIS the decision makers use the linguisticvariables to evaluate each alternative with respect to eachcriterion in order to assess the importance of the criteriaThe linguistic variables are converted into triangular


Table 12 Maintenance function ranking and performance index ranking using fuzzy TOPSIS

Function number Maintenance function 119863120582+

120572119863120582minus

120572

Separation scoreCC119894

Ranking

1 Fog seal 00580 00220 02750 72 Micro surfacing 00497 00485 04255 53 Slurry seal 00310 00270 04655 34 Cape seal 00459 00340 03921 65 Chip seal 00378 00291 04350 46 Thin HMA overlay 00347 00420 05480 17 Resurfacing 00432 00477 05248 2

0002004006008

01012014016018

02

1 2 3 4 5 6 7Maintenance function

Stan

dard

ized

rank

ing

inde

x

Fuzzy AHPFuzzy TOPSISManual ranking

Figure 10 Comparison of maintenance prioritization results fromfuzzy AHP and fuzzy TOPSIS

fuzzy numbers from which the fuzzy decision matrix isdetermined The normalized fuzzy decision matrix andthe weighted normalized fuzzy decision matrix are thenformed After determining the FPIS and FNIS the distance(119889) of each alternative to FPIS and FNIS is also determinedTherefrom the closeness coefficient of each alternative isindividually computed From the seven alternatives thecloseness coefficient revealed the results in Table 12 for thefuzzy TOPSIS and in Table 11 for the fuzzy AHP

The fundamental differences between these two methodscould be based on the fact that TOPSIS considers the lin-guistic variables at the onset of the pairwise comparison andtherefore the results are not affected by the AHP drawbacksin fuzzy AHP Nonetheless according to the results the topthree results were similar for both methods This in partshows that apart from the subjectivity that is not criticallycaptured by AHP in the pairwise comparison process bothTOPSIS and AHP as multicriteria decision making tech-niques are completive in performance But as presented inFigure 10 the subjectivity in AHP is noticed when the resultsare compared on standardized scale

In overall the appropriate preventive maintenance strat-egy will largely be influenced by the type severity andextent of the pavement surface distresses and the structuraland functional condition of the pavement In this regard

the influences of the categories of pavement maintenanceand the performance of preventive maintenance treatmentsas recommended by Johanns and Craig [42] should betaken into consideration in balancing between preventivecorrective and emergency maintenances schedules

6 Conclusions

The current case study presents a methodological overviewon the use of multiattribute decision making using fuzzyAHP and fuzzy TOPSIS for the prioritization of pavementmaintenance alternatives By using different sets of fuzzymembership functions the current approach enables deci-sion makers to capture the often unpredictable and complexpavement maintenance prioritization procedure in a moreobjective way

For the case study it is observed that maintenancemeasures relate to the following pavement failures crackingpotholes raveling and patching From the prioritizationresults and with manual-based opinion it is concluded thatthe top three maintenance objective functions in the casestudy urban roads are characterized by Thin HMA overlayresurfacing and slurry seals for the following pavementmaintenance objectives road safety conditions pavementsurface preservation road operational status and standardsand the road aesthetics The results show that road safety isclosely related to the actual pavement preservation status andboth contribute in nearly the same ratio to more than 60 ofthe maintenance objectives

The ranking procedures yielded nearly similar resultswith fuzzy TOPSIS performing slightly better than fuzzyAHP when the results were compared against actualempirical-manual-based prioritization Further the resultsshow that at optimal degrees of confidence and risk thefuzzy AHP tended to overestimate the prioritization rankingprocess as compared to the fuzzy TOPSIS approach

To improve on the current study it is recommended thatautomated distress surveys andmeasurements be consideredThis is important in improving on the speeds of conditionsurveys accuracy and reliability and cost-effectivenessDevelopments on pavement maintenance prioritizationapproach that can enable decision makers to quantify andminimize the total risk due to canceling or deferring mainte-nance functions during budget cuts should also be consideredin the prioritization process Additionally studies on the


spatial-temporalmodelling of the rate of pavement deteriora-tion are recommended in order to integrate the maintenanceprioritization approach with the assetrsquos whole-life economicanalysis And in addition detailed studies on the variationsand relationships between the decision makersrsquo levelof confidence and attitude to risk in multicriteria decisionmaking process can also be a detailed subject of investigation

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

The authors would like to acknowledge all those who wereinvolved in the field surveys on the road condition inspectionproject Further acknowledgements go to the contributionsin terms of comments by the anonymous reviewers who tooktheir time to pinpoint key areas to improve on in this paper

References

[1] L Sun and W Gu ldquoPavement condition assessment usingfuzzy logic theory and analytic hierarchy processrdquo Journal ofTransportation Engineering vol 137 no 9 pp 648ndash655 2011

[2] S Cafiso A Graziano and S Battiato ldquoEvaluation of pavementsurface distress using digital image collection and analysisrdquo inProceedings of the 7th International Congress on Advances inCivil Engineering p 10 Yildiz Technical University IstanbulTurkey October 2006

[3] YU Shah S S Jain andM Parida ldquoEvaluation of prioritizationmethods for effective pavement maintenance of urban roadsrdquoInternational Journal of Pavement Engineering vol 15 no 3 pp238ndash250 2014

[4] T L Saaty ldquoA scaling method for priorities in hierarchicalstructuresrdquo Journal of Mathematical Psychology vol 15 no 3pp 234ndash281 1977

[5] T L Saaty Multi-Criteria Decision Making The Analytic Hier-archy Process McGraw-Hill New York NY USA 1980

[6] P K Agarwal A Das and P Chakroborty ldquoA rational approachof prioritization of highway sections for maintenancerdquo inProceedings of the 6th International Conference on ManagingPavements p 12 Brisbane Australia October 2004

[7] J Farhan and T F Fwa ldquoPavement maintenance prioritiza-tion using analytic hierarchy processrdquo Transportation ResearchRecord vol 2093 pp 12ndash24 2009

[8] W Liu and Z Zhang ldquoPrioritization of highway maintenancefunctions using multi-attribute decision making with fuzzypairwise comparisonrdquo Tech Rep SWUTC11161128ndash1 Centerfor Transportation Research University of Texas Austin TexUSA 2012

[9] H Deng ldquoMulti-criteria analysis with fuzzy pairwise Compari-sonrdquo International Journal of Approximate Reasoning vol 21 no3 pp 215ndash231 1999

[10] L A Zadeh ldquoFuzzy setsrdquo Information and Computation vol 8pp 338ndash353 1965

[11] J Efstathiou ldquoPractical multi-attribute decision-making andfuzzy set theoryrdquo in TIMSStudies in Management Science vol20 pp 307ndash320 Elsevier 1984

[12] D Dubois and H Prade ldquoRecent models of uncertainty andimprecision as a basis for decision theory toward less normativeframeworksrdquo in Intelligent Decision Support in Process Environ-ments E Hollnagel G Mancini and D Woods Eds pp 3ndash24Springer Berlin Germany 1985

[13] S J Chen and C L Hwang Fuzzy Multiple Attribute DecisionMaking Methods and Applications Springer New York NYUSA 1992

[14] H-J Zimmermann Fuzzy Set Theory and Its ApplicationsKluwer Academic Boston Mass USA 1996

[15] M Kordi and S A Brandt ldquoEffects of increasing fuzzinesson analytic hierarchy process for spatial multicriteria decisionanalysisrdquo Computers Environment and Urban Systems vol 36no 1 pp 43ndash53 2012

[16] LMikhailov ldquoDeriving priorities from fuzzy pairwise compari-son judgementsrdquo Fuzzy Sets and Systems vol 134 no 3 pp 365ndash385 2003

[17] D Moazami and R Muniandy ldquoFuzzy inference and multi-criteria decision making applications in pavement rehabilita-tion prioritizationrdquo Australian Journal of Basic and AppliedSciences vol 4 no 10 pp 4740ndash4748 2010

[18] C L Hwang and K Yoon Multiple Attribute Decision MakingMethods and Applications A State-of-the-Art Survey SpringerNew York NY USA 1981

[19] C LHwang andK S YoonMultiple Attribute DecisionMakingMethods and Applications Springer Berlin Germany 1981

[20] A Vega J Aguaron J Garcıa-Alcaraz and J M Moreno-Jimenez ldquoNotes on dependent attributes in TOPSISrdquo ProcediaComputer Science vol 31 pp 308ndash317 2014

[21] K C P Wang C Nunn C Mackey et al ldquoNetwork levelcrack survey with the automated real-time distress analyzerrdquoin Proceedings of the 83rd Annual Meeting of TransportationResearch Board (TRB rsquo03) CD-ROM p 22 2003

[22] N Bandara and M Gunaratne ldquoCurrent and future pavementmaintenance prioritization based on rapid visual conditionevaluationrdquo Journal of Transportation Engineering vol 127 no2 pp 116ndash123 2001

[23] F Zahedi ldquoThe analytic hierarchy process a survey of themethod and its applicationsrdquo Interfaces vol 16 no 4 pp 96ndash108 1996

[24] O S Vaidya and S Kumar ldquoAnalytic hierarchy process anoverview of applicationsrdquo European Journal of OperationalResearch vol 169 no 1 pp 1ndash29 2006

[25] Y Ouma and R Tateishi ldquoUrban flood vulnerability and riskmapping using integrated multi-parametric AHP and GISmethodological overview and case study assessmentrdquo Watervol 6 no 6 pp 1515ndash1545 2014

[26] T L Saaty ldquoDecision making with analytic hierarchy processrdquoInternational Journal of Services Sciences vol 1 no 1 pp 83ndash982008

[27] S H Chen and C H Hsieh ldquoRepresentation ranking distanceand similarity of L-R type fuzzy number and applicationrdquoAustralian Journal of Intelligent Information Processing Systemsvol 6 no 4 pp 217ndash229 2000

[28] M T Tang G H Tzeng and S W Wang ldquoA hierarchy fuzzyMCDM method for studying electronic marketing strategiesin the information service industryrdquo Journal of InternationalInformation Management vol 8 no 1 pp 1ndash22 1999

[29] D-Y Chang ldquoApplications of the extent analysis method onfuzzy AHPrdquo European Journal of Operational Research vol 95no 3 pp 649ndash655 1996


[30] R Aggarwal and S Singh ldquoAHP and extent fuzzy AHPapproach for prioritization of performance measurementattributesrdquo International Journal of Social Education Economicsand Management Engineering vol 7 no 1 pp 43ndash48 2013

[31] Y O Ouma C Yabann M Kirichu and R Tateishi ldquoOpti-mization of urban highway bypass horizontal alignment amethodological overview of intelligent spatialMCDA approachusing fuzzy AHP and GISrdquo Advances in Civil Engineering vol2014 Article ID 182568 26 pages 2014

[32] A Kaufmann and M M Gupta Introduction to Fuzzy Arith-metic Theory and Applications Van Nostrand Reinhold NewYork NY USA 1991

[33] M B Javanbarg C Scawthorn J Kiyono and B Shah-bodaghkhan ldquoFuzzy AHP-based multicriteria decision makingsystems using particle swarm optimizationrdquo Expert Systemswith Applications vol 39 no 1 pp 960ndash966 2012

[34] J J Buckley ldquoFuzzy hierarchical analysisrdquo Fuzzy Sets andSystems vol 17 no 3 pp 233ndash247 1985

[35] T-Y Hsieh S-T Lu andG-H Tzeng ldquoFuzzyMCDMapproachfor planning and design tenders selection in public officebuildingsrdquo International Journal of Project Management vol 22no 7 pp 573ndash584 2004

[36] G R Jahanshahloo F H Lotfi andM Izadikhah ldquoAn algorith-mic method to extend TOPSIS for decision-making problemswith interval datardquo Applied Mathematics and Computation vol175 no 2 pp 1375ndash1384 2006

[37] T-C Wang and T-H Chang ldquoApplication of TOPSIS inevaluating initial training aircraft under a fuzzy environmentrdquoExpert Systems with Applications vol 33 no 4 pp 870ndash8802007

[38] I Ertugrul and N Karakasoglu ldquoPerformance evaluation ofTurkish cement firms with fuzzy analytic hierarchy process andTOPSISmethodsrdquo Expert Systems with Applications vol 36 no1 pp 702ndash715 2009

[39] M Ashrafzadeh F R Mokhatab and N I Mollaverdi ldquoAppli-cation of fuzzy TOPSIS method for selection of warehouselocation a case studyrdquo Interdisciplinary Journal of ContemporaryResearch Business vol 3 no 9 pp 655ndash671 2012

[40] C-C Sun ldquoA performance evaluation model by integratingfuzzy AHP and fuzzy TOPSIS methodsrdquo Expert Systems withApplications vol 37 no 12 pp 7745ndash7754 2010

[41] C-T Chen C-T Lin and S-F Huang ldquoA fuzzy approach forsupplier evaluation and selection in supply chainmanagementrdquoInternational Journal of Production Economics vol 102 no 2 pp289ndash301 2006

[42] M Johanns and J Craig Pavement Maintenance ManualNDOR Grand Island Neb USA 2002

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014


Active and Passive Electronic Components

Control Scienceand Engineering

Journal of



RotatingMachinery


Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design



Shock and Vibration


Civil EngineeringAdvances in

Acoustics and VibrationAdvances in



Electrical and Computer Engineering

Journal of

Advances inOptoElectronics


Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of


Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014


Chemical EngineeringInternational Journal of Antennas and

Propagation




Navigation and Observation



DistributedSensor Networks



PMMS Pavement maintenance

Pavement construction

Pavement design

Pavement planning

Pavement evaluation

Pavement research

Bridges Side walk Traffic signs

PMS

MampR

Road furniture

Figure 1 Schematic structure of a typical pavement management system (PMS) and pavement maintenance and management system(PMMS)

introduced by Saaty in the 1970s [4 5] Saaty developed AHPto primarily meet the complexities and challenges of decisionsituations that are brought out by multiple and conflictingcriteria as a multicriteria decision making (MCDM) toolAHP aids decisionmakers in determining the best criteria outof multiple sets of criteria based on crisp or exact numericalvalues

On road pavement maintenance priority ranking andanalysis AHP has been widely used (eg [6 7]) Howeverdue to the fact that in most practical situations the humanpreference is marred by uncertainty decision makers wouldfind it difficult to explicitly assign exact numerical valuesto the comparison judgments [8] Therefore the decisionmaker would theoretically find it very difficult to express thestrength of his preferences and confidence in terms of theAHP in pairwise comparison judgments As such AHP hasbeen argued to be ineffective when employed to ambiguousor vaguely represented real-life problems that consist ofuncertainty and subjectivity [9]

In decision making processes uncertainty imprecisionand subjectivity can be handled by means of probabilitytheory and or fuzzy set theory (FST) [10] While probabilityfocuses on the stochasticity of the decision making processFST tends to formalize the subjective and imprecise natureof human behavior by representing and quantifying vagueinformation through a membership grade function [10]As such probabilistic theory is not adequately suited forsubjectivity and imprecision in the human decision makingprocess [11ndash14]

The advantage of fuzzy based pairwise comparison isthat it allows decision makers to be more flexible in theirjudgments This is attained through the different degreesof fuzzification Furthermore if there is need for consider-ation of the attitude toward risk FTS has the possibility ofoverlapping preferences of criteria in case the expert is notconfident about the degree of importance within a set ofdecisions and there is the provision for interval decision asexpressed by a fuzzy membership function [15] FST can alsobe considered useful in decision problems where the degreesof uncertainty are expected to increase or change in time

for example in pavement failure and deterioration wheredifferent conditions are expected to change with time butthere is no predictive information on the future state

In order to accommodate uncertainty in expertsrsquo heuristicand experiential judgments Shah et al [3] used the rankingof road maintenance factors based on subjective rating Andto take care of subjectivity in judgment fuzzy pairwisecomparison deduction technique can be integratedwithAHP[3 16 17] Used independently fuzzy AHP results are directlyranked according to the normalized weights However inreal life decision decision makersrsquo degrees of confidence andattitudes to risks should be taken into consideration

Fuzzy Technique for Order Preference by Ideal Situation(TOPSIS) technique operates on the basis that the most pre-ferred decision alternative should not only have the shortestdistance from a positive ideal solution (PIS) but also havethe farthest distance from the negative ideal solution (NIS)hence its capability and efficiency in handling uncertainty[18 19] However the use of EuclideanDistance as determinedfrom PIS and NIS in TOPSIS does not consider the corre-lation of attributes and that makes it difficult to derive theweights of the decision attributes while keeping the judgmentconsistency [20] Thus the integration fuzzy TOPSIS withAHP is considered in this study in addition to taking intoaccount the degree of confidence in decision making

In this study fuzzy approach allowing experts to uselinguistic variables is considered for prioritization by apply-ing and comparing the results from fuzzy AHP and fuzzyTOPSISThe classical AHP is utilized to determine theweightvector of road maintenance factors with respect to the setobjectives In principle therefore the two approaches differprimarily in the way the fuzzy ratings are aggregated andnormalized but do impact on the data collection procedure

First a methodological overview and approach for fuzzyAHP and fuzzy TOPSIS for the formulation and automationof cost-effective PMMS for consistent and reliable prior-itization of MampR of road pavements in urban areas arepresented In the implementation a case study in EldoretTown in Kenya is used For thematic display of the roadnetwork a graphical user interface was designed in GIS and





(SRI)









(W)



























0 02 04 08 12 16

(km) N

E

S

W















3 Methodology


119894119895repre-






119860 =

[[[[[[

[

11988611 11988612 sdot sdot sdot 1198861119899

11988621 11988622 sdot sdot sdot 1198862119899

1198861198991 1198861198992 sdot sdot sdot 119886

119899119899

]]]]]]

]

(2)


119894119895for all 119894 119895 isin 1 2 119899


119896

119894119895is the





600ndash900








2 700ndash3 000





119886119894119895= (119886

1119894119895lowast 119886


119896


ℎ

119894119895)1ℎ

= (

ℎ

prod

119896=1

119886119896

119894119895)

1ℎ

(3)


1015840) (ii)













Rutting


(g) Patching







0

1

Am1 m2 m3

120583A

Ar(y) Ar(y)

(a)

1

V(A

2geA

1)

M2 M1

l2 m2 l1 d u2 m1 u1

(b)
















120583119860(119909) =

(119909 minus119897

119898minus 119897) 119897 le 119909 le 119898

(119906 minus119909

119906minus 119898) 119898 le 119909 le 119906

0 otherwise

(4)

where 119897 (= 1198981) and 119906 (= 119898






119860 = (119860119897(119910)

119860119903(119910)

)

= (1198981 + (1198982 minus1198981) 1199101198983 + (1198982 minus1198983) 119910)


(5)



following

119860 = (119886119894119895) =

[[[[[[

[

(1 1 1) 11988612 sdot sdot sdot 1198861119899

11988621 (1 1 1) sdot sdot sdot 1198862119899

1198861198991 119886


]]]]]]

]

(6)



(a)







(b)


In general 119886119894119895= (119897119894119895 119898119894119895 119906119894119895) with 119897


119894119895


119894119895=



1198601 oplus1198602 = (1198971 + 1198972 1198981 +1198982 1199061 +1199062) (7)

1198601 otimes1198602 = (11989711198972 11989811198982 11990611199062) (8)

119860minus11 = (

11199061

11198981

11198971) (9)


119894119895 such

that if 119886119894119895

= 1 then 119886119894119895

= 1119886119895119894for all 119894 119895 le 119899 where 119899












119894119895 as given in

(6)



119886119894119896

otimes 119886119896119895








119894119899)1119899



119899]minus1

(10)

where 119886119894119895





119894= (119897119908119894 119898119908119894 119906119908119894) [35]


119894= sum119899



is the alternative







119894119894 =



119895119895 = 1


denoted by 119896= 119909119894119895119896


119896(119909)


= (119886 119887 119888) where 119896 = 1 2 119870 where

119886 = min119896

119886119896

119887 =1119870

119870

sum

119896=1119887119896

119888 = max119896

119888119896

(11)



are119908119894119895119896

= (1199081198941119896

1199081198942119896

1199081198943119896


by 119909119894119895= (119886119894119895 119887119894119895 119888119894119895) where

119886119894119895= min119896

119886119894119895119896

119887119894119895=

1119870

119870

sum

119896=1119887119894119895119896

119888119894119895= max119896

119888119894119895119896

(12)




1199081198951 = min

119896

1199081198951198961

1199081198952 =

1119870

119870

sum

119896=11199081198951198962

1199081198953 = max

119896

1199081198951198963

(13)


119863 =

1198621 1198622 sdot sdot sdot 119862119899

1198601

1198602

119860119898

[[[[[

[

11990911

11990921

sdot sdot sdot

1199091198981

11990912

11990922

sdot sdot sdot

1199091198981

sdot sdot sdot

sdot sdot sdot

sdot sdot sdot

sdot sdot sdot

1199091119899

11990921

sdot sdot sdot

119909119898119899

]]]]]

]

(14)

where 119909119894119895= (1119870)(119909


119896


119870

119894119895) with 119909

119896

119894119895being


119895as


= (119897119896

119894119895 119898119896

119894119895 119906119896

119894119895) and

= (1199081 1199082 119908119899) [40]


= [119903119894119895]119898times119899

119894 = 1 2 119898 119895 = 1 2 119899 (15)

where 119903119894119895= (119886119894119895119888lowast

119895 119887119894119895119888lowast

119895 119888119894119895119888lowast

119895) and 119888

lowast

119895= max

119894119888119894119895are called


119895119888lowast

119895 119886minus

119895119887lowast

119895 119886minus

119895119886lowast

119895) and 119886

minus

119895=





= [V119894119895]119898times119899

= [119903119894119895 (sdot) 119908119894119895]

119894 = 1 2 119898 119895 = 1 2 119899(16)


119894119895


119860+= (V+1 V

+

2 V+

119899)

where V+119895= max119894

V1198941198953 119894 = 1 2 119898 119895 = 1 2 119899


minus

2 Vminus

119899)


V1198941198951 119894 = 1 2 119898 119895 = 1 2 119899

(17)


119894 119889minus



119889+

119894=

119899

sum

119895=1119889V (V119894119895 V

+

119895) = [

[

13

119899

sum

119895=1(V119894119895minus V+119895)2]

]

12

119894 = 1 2 119898

119889minus

119894=

119899

sum

119895=1119889V (V119894119895 V

minus

119895) = [

[

13

119899

sum

119895=1(V119894119895minus Vminus119895)2]

]

12

119894 = 1 2 119898

(18)






minus)


CC119894=

119889minus

119894

119889minus

119894+ 119889+

119894

= (1minus119889+

119894

119889minus

119894+ 119889+

119894

)

for 119894 = 1 2 119898

(19)


119894+ 119889+



119894(119889minus

119894+119889+


alternative








surfacingSlurryseal


overlay Resurfacing

Rutting times times






2+400

2+100





0

2

4

6

8

10

12

Poth

oles

Long

itudi

nal

crac

ks

Tran

sver

secr

acks

Alli

gato

rcr

acki

ng

crac

king

Bloc

k

Rave

ling

Patc

hing

Occ

urre

nce o

f dist

ress



(0+000

ndash3+000

km)










































120582

120572


119885120582

120572=

RS PSR ROS RA100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816


(0170)


(0142)


(0161)


(0229)

100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816

(20)





(MampR) functions


(ROS)

Fog seal

Micro surfacing

Slurry seal

Cape seal

Chip seal

Thin HMA overlay

Resurfacing


Road safety (RS)

Road aesthetics(RA)






1 Fog seal 0755 7















120572119863120582minus

120572


Ranking


0002004006008

01012014016018

02


Stan

dard

ized

rank

ing

inde

x







6 Conclusions









Acknowledgments


References














































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation













(SRI)









(W)



























0 02 04 08 12 16

(km) N

E

S

W















3 Methodology


119894119895repre-






119860 =

[[[[[[

[

11988611 11988612 sdot sdot sdot 1198861119899

11988621 11988622 sdot sdot sdot 1198862119899

1198861198991 1198861198992 sdot sdot sdot 119886

119899119899

]]]]]]

]

(2)


119894119895for all 119894 119895 isin 1 2 119899


119896

119894119895is the





600ndash900








2 700ndash3 000





119886119894119895= (119886

1119894119895lowast 119886


119896


ℎ

119894119895)1ℎ

= (

ℎ

prod

119896=1

119886119896

119894119895)

1ℎ

(3)


1015840) (ii)













Rutting


(g) Patching







0

1

Am1 m2 m3

120583A

Ar(y) Ar(y)

(a)

1

V(A

2geA

1)

M2 M1

l2 m2 l1 d u2 m1 u1

(b)
















120583119860(119909) =

(119909 minus119897

119898minus 119897) 119897 le 119909 le 119898

(119906 minus119909

119906minus 119898) 119898 le 119909 le 119906

0 otherwise

(4)

where 119897 (= 1198981) and 119906 (= 119898






119860 = (119860119897(119910)

119860119903(119910)

)

= (1198981 + (1198982 minus1198981) 1199101198983 + (1198982 minus1198983) 119910)


(5)



following

119860 = (119886119894119895) =

[[[[[[

[

(1 1 1) 11988612 sdot sdot sdot 1198861119899

11988621 (1 1 1) sdot sdot sdot 1198862119899

1198861198991 119886


]]]]]]

]

(6)



(a)







(b)


In general 119886119894119895= (119897119894119895 119898119894119895 119906119894119895) with 119897


119894119895


119894119895=



1198601 oplus1198602 = (1198971 + 1198972 1198981 +1198982 1199061 +1199062) (7)

1198601 otimes1198602 = (11989711198972 11989811198982 11990611199062) (8)

119860minus11 = (

11199061

11198981

11198971) (9)


119894119895 such

that if 119886119894119895

= 1 then 119886119894119895

= 1119886119895119894for all 119894 119895 le 119899 where 119899












119894119895 as given in

(6)



119886119894119896

otimes 119886119896119895








119894119899)1119899



119899]minus1

(10)

where 119886119894119895





119894= (119897119908119894 119898119908119894 119906119908119894) [35]


119894= sum119899



is the alternative







119894119894 =



119895119895 = 1


denoted by 119896= 119909119894119895119896


119896(119909)


= (119886 119887 119888) where 119896 = 1 2 119870 where

119886 = min119896

119886119896

119887 =1119870

119870

sum

119896=1119887119896

119888 = max119896

119888119896

(11)



are119908119894119895119896

= (1199081198941119896

1199081198942119896

1199081198943119896


by 119909119894119895= (119886119894119895 119887119894119895 119888119894119895) where

119886119894119895= min119896

119886119894119895119896

119887119894119895=

1119870

119870

sum

119896=1119887119894119895119896

119888119894119895= max119896

119888119894119895119896

(12)




1199081198951 = min

119896

1199081198951198961

1199081198952 =

1119870

119870

sum

119896=11199081198951198962

1199081198953 = max

119896

1199081198951198963

(13)


119863 =

1198621 1198622 sdot sdot sdot 119862119899

1198601

1198602

119860119898

[[[[[

[

11990911

11990921

sdot sdot sdot

1199091198981

11990912

11990922

sdot sdot sdot

1199091198981

sdot sdot sdot

sdot sdot sdot

sdot sdot sdot

sdot sdot sdot

1199091119899

11990921

sdot sdot sdot

119909119898119899

]]]]]

]

(14)

where 119909119894119895= (1119870)(119909


119896


119870

119894119895) with 119909

119896

119894119895being


119895as


= (119897119896

119894119895 119898119896

119894119895 119906119896

119894119895) and

= (1199081 1199082 119908119899) [40]


= [119903119894119895]119898times119899

119894 = 1 2 119898 119895 = 1 2 119899 (15)

where 119903119894119895= (119886119894119895119888lowast

119895 119887119894119895119888lowast

119895 119888119894119895119888lowast

119895) and 119888

lowast

119895= max

119894119888119894119895are called


119895119888lowast

119895 119886minus

119895119887lowast

119895 119886minus

119895119886lowast

119895) and 119886

minus

119895=





= [V119894119895]119898times119899

= [119903119894119895 (sdot) 119908119894119895]

119894 = 1 2 119898 119895 = 1 2 119899(16)


119894119895


119860+= (V+1 V

+

2 V+

119899)

where V+119895= max119894

V1198941198953 119894 = 1 2 119898 119895 = 1 2 119899


minus

2 Vminus

119899)


V1198941198951 119894 = 1 2 119898 119895 = 1 2 119899

(17)


119894 119889minus



119889+

119894=

119899

sum

119895=1119889V (V119894119895 V

+

119895) = [

[

13

119899

sum

119895=1(V119894119895minus V+119895)2]

]

12

119894 = 1 2 119898

119889minus

119894=

119899

sum

119895=1119889V (V119894119895 V

minus

119895) = [

[

13

119899

sum

119895=1(V119894119895minus Vminus119895)2]

]

12

119894 = 1 2 119898

(18)






minus)


CC119894=

119889minus

119894

119889minus

119894+ 119889+

119894

= (1minus119889+

119894

119889minus

119894+ 119889+

119894

)

for 119894 = 1 2 119898

(19)


119894+ 119889+



119894(119889minus

119894+119889+


alternative








surfacingSlurryseal


overlay Resurfacing

Rutting times times






2+400

2+100





0

2

4

6

8

10

12

Poth

oles

Long

itudi

nal

crac

ks

Tran

sver

secr

acks

Alli

gato

rcr

acki

ng

crac

king

Bloc

k

Rave

ling

Patc

hing

Occ

urre

nce o

f dist

ress



(0+000

ndash3+000

km)










































120582

120572


119885120582

120572=

RS PSR ROS RA100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816


(0170)


(0142)


(0161)


(0229)

100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816

(20)





(MampR) functions


(ROS)

Fog seal

Micro surfacing

Slurry seal

Cape seal

Chip seal

Thin HMA overlay

Resurfacing


Road safety (RS)

Road aesthetics(RA)






1 Fog seal 0755 7















120572119863120582minus

120572


Ranking


0002004006008

01012014016018

02


Stan

dard

ized

rank

ing

inde

x







6 Conclusions









Acknowledgments


References














































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation























0 02 04 08 12 16

(km) N

E

S

W















3 Methodology


119894119895repre-






119860 =

[[[[[[

[

11988611 11988612 sdot sdot sdot 1198861119899

11988621 11988622 sdot sdot sdot 1198862119899

1198861198991 1198861198992 sdot sdot sdot 119886

119899119899

]]]]]]

]

(2)


119894119895for all 119894 119895 isin 1 2 119899


119896

119894119895is the





600ndash900








2 700ndash3 000





119886119894119895= (119886

1119894119895lowast 119886


119896


ℎ

119894119895)1ℎ

= (

ℎ

prod

119896=1

119886119896

119894119895)

1ℎ

(3)


1015840) (ii)













Rutting


(g) Patching







0

1

Am1 m2 m3

120583A

Ar(y) Ar(y)

(a)

1

V(A

2geA

1)

M2 M1

l2 m2 l1 d u2 m1 u1

(b)
















120583119860(119909) =

(119909 minus119897

119898minus 119897) 119897 le 119909 le 119898

(119906 minus119909

119906minus 119898) 119898 le 119909 le 119906

0 otherwise

(4)

where 119897 (= 1198981) and 119906 (= 119898






119860 = (119860119897(119910)

119860119903(119910)

)

= (1198981 + (1198982 minus1198981) 1199101198983 + (1198982 minus1198983) 119910)


(5)



following

119860 = (119886119894119895) =

[[[[[[

[

(1 1 1) 11988612 sdot sdot sdot 1198861119899

11988621 (1 1 1) sdot sdot sdot 1198862119899

1198861198991 119886


]]]]]]

]

(6)



(a)







(b)


In general 119886119894119895= (119897119894119895 119898119894119895 119906119894119895) with 119897


119894119895


119894119895=



1198601 oplus1198602 = (1198971 + 1198972 1198981 +1198982 1199061 +1199062) (7)

1198601 otimes1198602 = (11989711198972 11989811198982 11990611199062) (8)

119860minus11 = (

11199061

11198981

11198971) (9)


119894119895 such

that if 119886119894119895

= 1 then 119886119894119895

= 1119886119895119894for all 119894 119895 le 119899 where 119899












119894119895 as given in

(6)



119886119894119896

otimes 119886119896119895








119894119899)1119899



119899]minus1

(10)

where 119886119894119895





119894= (119897119908119894 119898119908119894 119906119908119894) [35]


119894= sum119899



is the alternative







119894119894 =



119895119895 = 1


denoted by 119896= 119909119894119895119896


119896(119909)


= (119886 119887 119888) where 119896 = 1 2 119870 where

119886 = min119896

119886119896

119887 =1119870

119870

sum

119896=1119887119896

119888 = max119896

119888119896

(11)



are119908119894119895119896

= (1199081198941119896

1199081198942119896

1199081198943119896


by 119909119894119895= (119886119894119895 119887119894119895 119888119894119895) where

119886119894119895= min119896

119886119894119895119896

119887119894119895=

1119870

119870

sum

119896=1119887119894119895119896

119888119894119895= max119896

119888119894119895119896

(12)




1199081198951 = min

119896

1199081198951198961

1199081198952 =

1119870

119870

sum

119896=11199081198951198962

1199081198953 = max

119896

1199081198951198963

(13)


119863 =

1198621 1198622 sdot sdot sdot 119862119899

1198601

1198602

119860119898

[[[[[

[

11990911

11990921

sdot sdot sdot

1199091198981

11990912

11990922

sdot sdot sdot

1199091198981

sdot sdot sdot

sdot sdot sdot

sdot sdot sdot

sdot sdot sdot

1199091119899

11990921

sdot sdot sdot

119909119898119899

]]]]]

]

(14)

where 119909119894119895= (1119870)(119909


119896


119870

119894119895) with 119909

119896

119894119895being


119895as


= (119897119896

119894119895 119898119896

119894119895 119906119896

119894119895) and

= (1199081 1199082 119908119899) [40]


= [119903119894119895]119898times119899

119894 = 1 2 119898 119895 = 1 2 119899 (15)

where 119903119894119895= (119886119894119895119888lowast

119895 119887119894119895119888lowast

119895 119888119894119895119888lowast

119895) and 119888

lowast

119895= max

119894119888119894119895are called


119895119888lowast

119895 119886minus

119895119887lowast

119895 119886minus

119895119886lowast

119895) and 119886

minus

119895=





= [V119894119895]119898times119899

= [119903119894119895 (sdot) 119908119894119895]

119894 = 1 2 119898 119895 = 1 2 119899(16)


119894119895


119860+= (V+1 V

+

2 V+

119899)

where V+119895= max119894

V1198941198953 119894 = 1 2 119898 119895 = 1 2 119899


minus

2 Vminus

119899)


V1198941198951 119894 = 1 2 119898 119895 = 1 2 119899

(17)


119894 119889minus



119889+

119894=

119899

sum

119895=1119889V (V119894119895 V

+

119895) = [

[

13

119899

sum

119895=1(V119894119895minus V+119895)2]

]

12

119894 = 1 2 119898

119889minus

119894=

119899

sum

119895=1119889V (V119894119895 V

minus

119895) = [

[

13

119899

sum

119895=1(V119894119895minus Vminus119895)2]

]

12

119894 = 1 2 119898

(18)






minus)


CC119894=

119889minus

119894

119889minus

119894+ 119889+

119894

= (1minus119889+

119894

119889minus

119894+ 119889+

119894

)

for 119894 = 1 2 119898

(19)


119894+ 119889+



119894(119889minus

119894+119889+


alternative








surfacingSlurryseal


overlay Resurfacing

Rutting times times






2+400

2+100





0

2

4

6

8

10

12

Poth

oles

Long

itudi

nal

crac

ks

Tran

sver

secr

acks

Alli

gato

rcr

acki

ng

crac

king

Bloc

k

Rave

ling

Patc

hing

Occ

urre

nce o

f dist

ress



(0+000

ndash3+000

km)










































120582

120572


119885120582

120572=

RS PSR ROS RA100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816


(0170)


(0142)


(0161)


(0229)

100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816

(20)





(MampR) functions


(ROS)

Fog seal

Micro surfacing

Slurry seal

Cape seal

Chip seal

Thin HMA overlay

Resurfacing


Road safety (RS)

Road aesthetics(RA)






1 Fog seal 0755 7















120572119863120582minus

120572


Ranking


0002004006008

01012014016018

02


Stan

dard

ized

rank

ing

inde

x







6 Conclusions









Acknowledgments


References














































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation
















3 Methodology


119894119895repre-






119860 =

[[[[[[

[

11988611 11988612 sdot sdot sdot 1198861119899

11988621 11988622 sdot sdot sdot 1198862119899

1198861198991 1198861198992 sdot sdot sdot 119886

119899119899

]]]]]]

]

(2)


119894119895for all 119894 119895 isin 1 2 119899


119896

119894119895is the





600ndash900








2 700ndash3 000





119886119894119895= (119886

1119894119895lowast 119886


119896


ℎ

119894119895)1ℎ

= (

ℎ

prod

119896=1

119886119896

119894119895)

1ℎ

(3)


1015840) (ii)













Rutting


(g) Patching







0

1

Am1 m2 m3

120583A

Ar(y) Ar(y)

(a)

1

V(A

2geA

1)

M2 M1

l2 m2 l1 d u2 m1 u1

(b)
















120583119860(119909) =

(119909 minus119897

119898minus 119897) 119897 le 119909 le 119898

(119906 minus119909

119906minus 119898) 119898 le 119909 le 119906

0 otherwise

(4)

where 119897 (= 1198981) and 119906 (= 119898






119860 = (119860119897(119910)

119860119903(119910)

)

= (1198981 + (1198982 minus1198981) 1199101198983 + (1198982 minus1198983) 119910)


(5)



following

119860 = (119886119894119895) =

[[[[[[

[

(1 1 1) 11988612 sdot sdot sdot 1198861119899

11988621 (1 1 1) sdot sdot sdot 1198862119899

1198861198991 119886


]]]]]]

]

(6)



(a)







(b)


In general 119886119894119895= (119897119894119895 119898119894119895 119906119894119895) with 119897


119894119895


119894119895=



1198601 oplus1198602 = (1198971 + 1198972 1198981 +1198982 1199061 +1199062) (7)

1198601 otimes1198602 = (11989711198972 11989811198982 11990611199062) (8)

119860minus11 = (

11199061

11198981

11198971) (9)


119894119895 such

that if 119886119894119895

= 1 then 119886119894119895

= 1119886119895119894for all 119894 119895 le 119899 where 119899












119894119895 as given in

(6)



119886119894119896

otimes 119886119896119895








119894119899)1119899



119899]minus1

(10)

where 119886119894119895





119894= (119897119908119894 119898119908119894 119906119908119894) [35]


119894= sum119899



is the alternative







119894119894 =



119895119895 = 1


denoted by 119896= 119909119894119895119896


119896(119909)


= (119886 119887 119888) where 119896 = 1 2 119870 where

119886 = min119896

119886119896

119887 =1119870

119870

sum

119896=1119887119896

119888 = max119896

119888119896

(11)



are119908119894119895119896

= (1199081198941119896

1199081198942119896

1199081198943119896


by 119909119894119895= (119886119894119895 119887119894119895 119888119894119895) where

119886119894119895= min119896

119886119894119895119896

119887119894119895=

1119870

119870

sum

119896=1119887119894119895119896

119888119894119895= max119896

119888119894119895119896

(12)




1199081198951 = min

119896

1199081198951198961

1199081198952 =

1119870

119870

sum

119896=11199081198951198962

1199081198953 = max

119896

1199081198951198963

(13)


119863 =

1198621 1198622 sdot sdot sdot 119862119899

1198601

1198602

119860119898

[[[[[

[

11990911

11990921

sdot sdot sdot

1199091198981

11990912

11990922

sdot sdot sdot

1199091198981

sdot sdot sdot

sdot sdot sdot

sdot sdot sdot

sdot sdot sdot

1199091119899

11990921

sdot sdot sdot

119909119898119899

]]]]]

]

(14)

where 119909119894119895= (1119870)(119909


119896


119870

119894119895) with 119909

119896

119894119895being


119895as


= (119897119896

119894119895 119898119896

119894119895 119906119896

119894119895) and

= (1199081 1199082 119908119899) [40]


= [119903119894119895]119898times119899

119894 = 1 2 119898 119895 = 1 2 119899 (15)

where 119903119894119895= (119886119894119895119888lowast

119895 119887119894119895119888lowast

119895 119888119894119895119888lowast

119895) and 119888

lowast

119895= max

119894119888119894119895are called


119895119888lowast

119895 119886minus

119895119887lowast

119895 119886minus

119895119886lowast

119895) and 119886

minus

119895=





= [V119894119895]119898times119899

= [119903119894119895 (sdot) 119908119894119895]

119894 = 1 2 119898 119895 = 1 2 119899(16)


119894119895


119860+= (V+1 V

+

2 V+

119899)

where V+119895= max119894

V1198941198953 119894 = 1 2 119898 119895 = 1 2 119899


minus

2 Vminus

119899)


V1198941198951 119894 = 1 2 119898 119895 = 1 2 119899

(17)


119894 119889minus



119889+

119894=

119899

sum

119895=1119889V (V119894119895 V

+

119895) = [

[

13

119899

sum

119895=1(V119894119895minus V+119895)2]

]

12

119894 = 1 2 119898

119889minus

119894=

119899

sum

119895=1119889V (V119894119895 V

minus

119895) = [

[

13

119899

sum

119895=1(V119894119895minus Vminus119895)2]

]

12

119894 = 1 2 119898

(18)






minus)


CC119894=

119889minus

119894

119889minus

119894+ 119889+

119894

= (1minus119889+

119894

119889minus

119894+ 119889+

119894

)

for 119894 = 1 2 119898

(19)


119894+ 119889+



119894(119889minus

119894+119889+


alternative








surfacingSlurryseal


overlay Resurfacing

Rutting times times






2+400

2+100





0

2

4

6

8

10

12

Poth

oles

Long

itudi

nal

crac

ks

Tran

sver

secr

acks

Alli

gato

rcr

acki

ng

crac

king

Bloc

k

Rave

ling

Patc

hing

Occ

urre

nce o

f dist

ress



(0+000

ndash3+000

km)










































120582

120572


119885120582

120572=

RS PSR ROS RA100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816


(0170)


(0142)


(0161)


(0229)

100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816

(20)





(MampR) functions


(ROS)

Fog seal

Micro surfacing

Slurry seal

Cape seal

Chip seal

Thin HMA overlay

Resurfacing


Road safety (RS)

Road aesthetics(RA)






1 Fog seal 0755 7















120572119863120582minus

120572


Ranking


0002004006008

01012014016018

02


Stan

dard

ized

rank

ing

inde

x







6 Conclusions









Acknowledgments


References














































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation




















Rutting


(g) Patching







0

1

Am1 m2 m3

120583A

Ar(y) Ar(y)

(a)

1

V(A

2geA

1)

M2 M1

l2 m2 l1 d u2 m1 u1

(b)
















120583119860(119909) =

(119909 minus119897

119898minus 119897) 119897 le 119909 le 119898

(119906 minus119909

119906minus 119898) 119898 le 119909 le 119906

0 otherwise

(4)

where 119897 (= 1198981) and 119906 (= 119898






119860 = (119860119897(119910)

119860119903(119910)

)

= (1198981 + (1198982 minus1198981) 1199101198983 + (1198982 minus1198983) 119910)


(5)



following

119860 = (119886119894119895) =

[[[[[[

[

(1 1 1) 11988612 sdot sdot sdot 1198861119899

11988621 (1 1 1) sdot sdot sdot 1198862119899

1198861198991 119886


]]]]]]

]

(6)



(a)







(b)


In general 119886119894119895= (119897119894119895 119898119894119895 119906119894119895) with 119897


119894119895


119894119895=



1198601 oplus1198602 = (1198971 + 1198972 1198981 +1198982 1199061 +1199062) (7)

1198601 otimes1198602 = (11989711198972 11989811198982 11990611199062) (8)

119860minus11 = (

11199061

11198981

11198971) (9)


119894119895 such

that if 119886119894119895

= 1 then 119886119894119895

= 1119886119895119894for all 119894 119895 le 119899 where 119899












119894119895 as given in

(6)



119886119894119896

otimes 119886119896119895








119894119899)1119899



119899]minus1

(10)

where 119886119894119895





119894= (119897119908119894 119898119908119894 119906119908119894) [35]


119894= sum119899



is the alternative







119894119894 =



119895119895 = 1


denoted by 119896= 119909119894119895119896


119896(119909)


= (119886 119887 119888) where 119896 = 1 2 119870 where

119886 = min119896

119886119896

119887 =1119870

119870

sum

119896=1119887119896

119888 = max119896

119888119896

(11)



are119908119894119895119896

= (1199081198941119896

1199081198942119896

1199081198943119896


by 119909119894119895= (119886119894119895 119887119894119895 119888119894119895) where

119886119894119895= min119896

119886119894119895119896

119887119894119895=

1119870

119870

sum

119896=1119887119894119895119896

119888119894119895= max119896

119888119894119895119896

(12)




1199081198951 = min

119896

1199081198951198961

1199081198952 =

1119870

119870

sum

119896=11199081198951198962

1199081198953 = max

119896

1199081198951198963

(13)


119863 =

1198621 1198622 sdot sdot sdot 119862119899

1198601

1198602

119860119898

[[[[[

[

11990911

11990921

sdot sdot sdot

1199091198981

11990912

11990922

sdot sdot sdot

1199091198981

sdot sdot sdot

sdot sdot sdot

sdot sdot sdot

sdot sdot sdot

1199091119899

11990921

sdot sdot sdot

119909119898119899

]]]]]

]

(14)

where 119909119894119895= (1119870)(119909


119896


119870

119894119895) with 119909

119896

119894119895being


119895as


= (119897119896

119894119895 119898119896

119894119895 119906119896

119894119895) and

= (1199081 1199082 119908119899) [40]


= [119903119894119895]119898times119899

119894 = 1 2 119898 119895 = 1 2 119899 (15)

where 119903119894119895= (119886119894119895119888lowast

119895 119887119894119895119888lowast

119895 119888119894119895119888lowast

119895) and 119888

lowast

119895= max

119894119888119894119895are called


119895119888lowast

119895 119886minus

119895119887lowast

119895 119886minus

119895119886lowast

119895) and 119886

minus

119895=





= [V119894119895]119898times119899

= [119903119894119895 (sdot) 119908119894119895]

119894 = 1 2 119898 119895 = 1 2 119899(16)


119894119895


119860+= (V+1 V

+

2 V+

119899)

where V+119895= max119894

V1198941198953 119894 = 1 2 119898 119895 = 1 2 119899


minus

2 Vminus

119899)


V1198941198951 119894 = 1 2 119898 119895 = 1 2 119899

(17)


119894 119889minus



119889+

119894=

119899

sum

119895=1119889V (V119894119895 V

+

119895) = [

[

13

119899

sum

119895=1(V119894119895minus V+119895)2]

]

12

119894 = 1 2 119898

119889minus

119894=

119899

sum

119895=1119889V (V119894119895 V

minus

119895) = [

[

13

119899

sum

119895=1(V119894119895minus Vminus119895)2]

]

12

119894 = 1 2 119898

(18)






minus)


CC119894=

119889minus

119894

119889minus

119894+ 119889+

119894

= (1minus119889+

119894

119889minus

119894+ 119889+

119894

)

for 119894 = 1 2 119898

(19)


119894+ 119889+



119894(119889minus

119894+119889+


alternative








surfacingSlurryseal


overlay Resurfacing

Rutting times times






2+400

2+100





0

2

4

6

8

10

12

Poth

oles

Long

itudi

nal

crac

ks

Tran

sver

secr

acks

Alli

gato

rcr

acki

ng

crac

king

Bloc

k

Rave

ling

Patc

hing

Occ

urre

nce o

f dist

ress



(0+000

ndash3+000

km)










































120582

120572


119885120582

120572=

RS PSR ROS RA100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816


(0170)


(0142)


(0161)


(0229)

100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816

(20)





(MampR) functions


(ROS)

Fog seal

Micro surfacing

Slurry seal

Cape seal

Chip seal

Thin HMA overlay

Resurfacing


Road safety (RS)

Road aesthetics(RA)






1 Fog seal 0755 7















120572119863120582minus

120572


Ranking


0002004006008

01012014016018

02


Stan

dard

ized

rank

ing

inde

x







6 Conclusions









Acknowledgments


References














































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










0

1

Am1 m2 m3

120583A

Ar(y) Ar(y)

(a)

1

V(A

2geA

1)

M2 M1

l2 m2 l1 d u2 m1 u1

(b)
















120583119860(119909) =

(119909 minus119897

119898minus 119897) 119897 le 119909 le 119898

(119906 minus119909

119906minus 119898) 119898 le 119909 le 119906

0 otherwise

(4)

where 119897 (= 1198981) and 119906 (= 119898






119860 = (119860119897(119910)

119860119903(119910)

)

= (1198981 + (1198982 minus1198981) 1199101198983 + (1198982 minus1198983) 119910)


(5)



following

119860 = (119886119894119895) =

[[[[[[

[

(1 1 1) 11988612 sdot sdot sdot 1198861119899

11988621 (1 1 1) sdot sdot sdot 1198862119899

1198861198991 119886


]]]]]]

]

(6)



(a)







(b)


In general 119886119894119895= (119897119894119895 119898119894119895 119906119894119895) with 119897


119894119895


119894119895=



1198601 oplus1198602 = (1198971 + 1198972 1198981 +1198982 1199061 +1199062) (7)

1198601 otimes1198602 = (11989711198972 11989811198982 11990611199062) (8)

119860minus11 = (

11199061

11198981

11198971) (9)


119894119895 such

that if 119886119894119895

= 1 then 119886119894119895

= 1119886119895119894for all 119894 119895 le 119899 where 119899












119894119895 as given in

(6)



119886119894119896

otimes 119886119896119895








119894119899)1119899



119899]minus1

(10)

where 119886119894119895





119894= (119897119908119894 119898119908119894 119906119908119894) [35]


119894= sum119899



is the alternative







119894119894 =



119895119895 = 1


denoted by 119896= 119909119894119895119896


119896(119909)


= (119886 119887 119888) where 119896 = 1 2 119870 where

119886 = min119896

119886119896

119887 =1119870

119870

sum

119896=1119887119896

119888 = max119896

119888119896

(11)



are119908119894119895119896

= (1199081198941119896

1199081198942119896

1199081198943119896


by 119909119894119895= (119886119894119895 119887119894119895 119888119894119895) where

119886119894119895= min119896

119886119894119895119896

119887119894119895=

1119870

119870

sum

119896=1119887119894119895119896

119888119894119895= max119896

119888119894119895119896

(12)




1199081198951 = min

119896

1199081198951198961

1199081198952 =

1119870

119870

sum

119896=11199081198951198962

1199081198953 = max

119896

1199081198951198963

(13)


119863 =

1198621 1198622 sdot sdot sdot 119862119899

1198601

1198602

119860119898

[[[[[

[

11990911

11990921

sdot sdot sdot

1199091198981

11990912

11990922

sdot sdot sdot

1199091198981

sdot sdot sdot

sdot sdot sdot

sdot sdot sdot

sdot sdot sdot

1199091119899

11990921

sdot sdot sdot

119909119898119899

]]]]]

]

(14)

where 119909119894119895= (1119870)(119909


119896


119870

119894119895) with 119909

119896

119894119895being


119895as


= (119897119896

119894119895 119898119896

119894119895 119906119896

119894119895) and

= (1199081 1199082 119908119899) [40]


= [119903119894119895]119898times119899

119894 = 1 2 119898 119895 = 1 2 119899 (15)

where 119903119894119895= (119886119894119895119888lowast

119895 119887119894119895119888lowast

119895 119888119894119895119888lowast

119895) and 119888

lowast

119895= max

119894119888119894119895are called


119895119888lowast

119895 119886minus

119895119887lowast

119895 119886minus

119895119886lowast

119895) and 119886

minus

119895=





= [V119894119895]119898times119899

= [119903119894119895 (sdot) 119908119894119895]

119894 = 1 2 119898 119895 = 1 2 119899(16)


119894119895


119860+= (V+1 V

+

2 V+

119899)

where V+119895= max119894

V1198941198953 119894 = 1 2 119898 119895 = 1 2 119899


minus

2 Vminus

119899)


V1198941198951 119894 = 1 2 119898 119895 = 1 2 119899

(17)


119894 119889minus



119889+

119894=

119899

sum

119895=1119889V (V119894119895 V

+

119895) = [

[

13

119899

sum

119895=1(V119894119895minus V+119895)2]

]

12

119894 = 1 2 119898

119889minus

119894=

119899

sum

119895=1119889V (V119894119895 V

minus

119895) = [

[

13

119899

sum

119895=1(V119894119895minus Vminus119895)2]

]

12

119894 = 1 2 119898

(18)






minus)


CC119894=

119889minus

119894

119889minus

119894+ 119889+

119894

= (1minus119889+

119894

119889minus

119894+ 119889+

119894

)

for 119894 = 1 2 119898

(19)


119894+ 119889+



119894(119889minus

119894+119889+


alternative








surfacingSlurryseal


overlay Resurfacing

Rutting times times






2+400

2+100





0

2

4

6

8

10

12

Poth

oles

Long

itudi

nal

crac

ks

Tran

sver

secr

acks

Alli

gato

rcr

acki

ng

crac

king

Bloc

k

Rave

ling

Patc

hing

Occ

urre

nce o

f dist

ress



(0+000

ndash3+000

km)










































120582

120572


119885120582

120572=

RS PSR ROS RA100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816


(0170)


(0142)


(0161)


(0229)

100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816

(20)





(MampR) functions


(ROS)

Fog seal

Micro surfacing

Slurry seal

Cape seal

Chip seal

Thin HMA overlay

Resurfacing


Road safety (RS)

Road aesthetics(RA)






1 Fog seal 0755 7















120572119863120582minus

120572


Ranking


0002004006008

01012014016018

02


Stan

dard

ized

rank

ing

inde

x







6 Conclusions









Acknowledgments


References














































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











(a)







(b)


In general 119886119894119895= (119897119894119895 119898119894119895 119906119894119895) with 119897


119894119895


119894119895=



1198601 oplus1198602 = (1198971 + 1198972 1198981 +1198982 1199061 +1199062) (7)

1198601 otimes1198602 = (11989711198972 11989811198982 11990611199062) (8)

119860minus11 = (

11199061

11198981

11198971) (9)


119894119895 such

that if 119886119894119895

= 1 then 119886119894119895

= 1119886119895119894for all 119894 119895 le 119899 where 119899












119894119895 as given in

(6)



119886119894119896

otimes 119886119896119895








119894119899)1119899



119899]minus1

(10)

where 119886119894119895





119894= (119897119908119894 119898119908119894 119906119908119894) [35]


119894= sum119899



is the alternative







119894119894 =



119895119895 = 1


denoted by 119896= 119909119894119895119896


119896(119909)


= (119886 119887 119888) where 119896 = 1 2 119870 where

119886 = min119896

119886119896

119887 =1119870

119870

sum

119896=1119887119896

119888 = max119896

119888119896

(11)



are119908119894119895119896

= (1199081198941119896

1199081198942119896

1199081198943119896


by 119909119894119895= (119886119894119895 119887119894119895 119888119894119895) where

119886119894119895= min119896

119886119894119895119896

119887119894119895=

1119870

119870

sum

119896=1119887119894119895119896

119888119894119895= max119896

119888119894119895119896

(12)




1199081198951 = min

119896

1199081198951198961

1199081198952 =

1119870

119870

sum

119896=11199081198951198962

1199081198953 = max

119896

1199081198951198963

(13)


119863 =

1198621 1198622 sdot sdot sdot 119862119899

1198601

1198602

119860119898

[[[[[

[

11990911

11990921

sdot sdot sdot

1199091198981

11990912

11990922

sdot sdot sdot

1199091198981

sdot sdot sdot

sdot sdot sdot

sdot sdot sdot

sdot sdot sdot

1199091119899

11990921

sdot sdot sdot

119909119898119899

]]]]]

]

(14)

where 119909119894119895= (1119870)(119909


119896


119870

119894119895) with 119909

119896

119894119895being


119895as


= (119897119896

119894119895 119898119896

119894119895 119906119896

119894119895) and

= (1199081 1199082 119908119899) [40]


= [119903119894119895]119898times119899

119894 = 1 2 119898 119895 = 1 2 119899 (15)

where 119903119894119895= (119886119894119895119888lowast

119895 119887119894119895119888lowast

119895 119888119894119895119888lowast

119895) and 119888

lowast

119895= max

119894119888119894119895are called


119895119888lowast

119895 119886minus

119895119887lowast

119895 119886minus

119895119886lowast

119895) and 119886

minus

119895=





= [V119894119895]119898times119899

= [119903119894119895 (sdot) 119908119894119895]

119894 = 1 2 119898 119895 = 1 2 119899(16)


119894119895


119860+= (V+1 V

+

2 V+

119899)

where V+119895= max119894

V1198941198953 119894 = 1 2 119898 119895 = 1 2 119899


minus

2 Vminus

119899)


V1198941198951 119894 = 1 2 119898 119895 = 1 2 119899

(17)


119894 119889minus



119889+

119894=

119899

sum

119895=1119889V (V119894119895 V

+

119895) = [

[

13

119899

sum

119895=1(V119894119895minus V+119895)2]

]

12

119894 = 1 2 119898

119889minus

119894=

119899

sum

119895=1119889V (V119894119895 V

minus

119895) = [

[

13

119899

sum

119895=1(V119894119895minus Vminus119895)2]

]

12

119894 = 1 2 119898

(18)






minus)


CC119894=

119889minus

119894

119889minus

119894+ 119889+

119894

= (1minus119889+

119894

119889minus

119894+ 119889+

119894

)

for 119894 = 1 2 119898

(19)


119894+ 119889+



119894(119889minus

119894+119889+


alternative








surfacingSlurryseal


overlay Resurfacing

Rutting times times






2+400

2+100





0

2

4

6

8

10

12

Poth

oles

Long

itudi

nal

crac

ks

Tran

sver

secr

acks

Alli

gato

rcr

acki

ng

crac

king

Bloc

k

Rave

ling

Patc

hing

Occ

urre

nce o

f dist

ress



(0+000

ndash3+000

km)










































120582

120572


119885120582

120572=

RS PSR ROS RA100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816


(0170)


(0142)


(0161)


(0229)

100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816

(20)





(MampR) functions


(ROS)

Fog seal

Micro surfacing

Slurry seal

Cape seal

Chip seal

Thin HMA overlay

Resurfacing


Road safety (RS)

Road aesthetics(RA)






1 Fog seal 0755 7















120572119863120582minus

120572


Ranking


0002004006008

01012014016018

02


Stan

dard

ized

rank

ing

inde

x







6 Conclusions









Acknowledgments


References














































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation













119894119895 as given in

(6)



119886119894119896

otimes 119886119896119895








119894119899)1119899



119899]minus1

(10)

where 119886119894119895





119894= (119897119908119894 119898119908119894 119906119908119894) [35]


119894= sum119899



is the alternative







119894119894 =



119895119895 = 1


denoted by 119896= 119909119894119895119896


119896(119909)


= (119886 119887 119888) where 119896 = 1 2 119870 where

119886 = min119896

119886119896

119887 =1119870

119870

sum

119896=1119887119896

119888 = max119896

119888119896

(11)



are119908119894119895119896

= (1199081198941119896

1199081198942119896

1199081198943119896


by 119909119894119895= (119886119894119895 119887119894119895 119888119894119895) where

119886119894119895= min119896

119886119894119895119896

119887119894119895=

1119870

119870

sum

119896=1119887119894119895119896

119888119894119895= max119896

119888119894119895119896

(12)




1199081198951 = min

119896

1199081198951198961

1199081198952 =

1119870

119870

sum

119896=11199081198951198962

1199081198953 = max

119896

1199081198951198963

(13)


119863 =

1198621 1198622 sdot sdot sdot 119862119899

1198601

1198602

119860119898

[[[[[

[

11990911

11990921

sdot sdot sdot

1199091198981

11990912

11990922

sdot sdot sdot

1199091198981

sdot sdot sdot

sdot sdot sdot

sdot sdot sdot

sdot sdot sdot

1199091119899

11990921

sdot sdot sdot

119909119898119899

]]]]]

]

(14)

where 119909119894119895= (1119870)(119909


119896


119870

119894119895) with 119909

119896

119894119895being


119895as


= (119897119896

119894119895 119898119896

119894119895 119906119896

119894119895) and

= (1199081 1199082 119908119899) [40]


= [119903119894119895]119898times119899

119894 = 1 2 119898 119895 = 1 2 119899 (15)

where 119903119894119895= (119886119894119895119888lowast

119895 119887119894119895119888lowast

119895 119888119894119895119888lowast

119895) and 119888

lowast

119895= max

119894119888119894119895are called


119895119888lowast

119895 119886minus

119895119887lowast

119895 119886minus

119895119886lowast

119895) and 119886

minus

119895=





= [V119894119895]119898times119899

= [119903119894119895 (sdot) 119908119894119895]

119894 = 1 2 119898 119895 = 1 2 119899(16)


119894119895


119860+= (V+1 V

+

2 V+

119899)

where V+119895= max119894

V1198941198953 119894 = 1 2 119898 119895 = 1 2 119899


minus

2 Vminus

119899)


V1198941198951 119894 = 1 2 119898 119895 = 1 2 119899

(17)


119894 119889minus



119889+

119894=

119899

sum

119895=1119889V (V119894119895 V

+

119895) = [

[

13

119899

sum

119895=1(V119894119895minus V+119895)2]

]

12

119894 = 1 2 119898

119889minus

119894=

119899

sum

119895=1119889V (V119894119895 V

minus

119895) = [

[

13

119899

sum

119895=1(V119894119895minus Vminus119895)2]

]

12

119894 = 1 2 119898

(18)






minus)


CC119894=

119889minus

119894

119889minus

119894+ 119889+

119894

= (1minus119889+

119894

119889minus

119894+ 119889+

119894

)

for 119894 = 1 2 119898

(19)


119894+ 119889+



119894(119889minus

119894+119889+


alternative








surfacingSlurryseal


overlay Resurfacing

Rutting times times






2+400

2+100





0

2

4

6

8

10

12

Poth

oles

Long

itudi

nal

crac

ks

Tran

sver

secr

acks

Alli

gato

rcr

acki

ng

crac

king

Bloc

k

Rave

ling

Patc

hing

Occ

urre

nce o

f dist

ress



(0+000

ndash3+000

km)










































120582

120572


119885120582

120572=

RS PSR ROS RA100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816


(0170)


(0142)


(0161)


(0229)

100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816

(20)





(MampR) functions


(ROS)

Fog seal

Micro surfacing

Slurry seal

Cape seal

Chip seal

Thin HMA overlay

Resurfacing


Road safety (RS)

Road aesthetics(RA)






1 Fog seal 0755 7















120572119863120582minus

120572


Ranking


0002004006008

01012014016018

02


Stan

dard

ized

rank

ing

inde

x







6 Conclusions









Acknowledgments


References














































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation












1199081198951 = min

119896

1199081198951198961

1199081198952 =

1119870

119870

sum

119896=11199081198951198962

1199081198953 = max

119896

1199081198951198963

(13)


119863 =

1198621 1198622 sdot sdot sdot 119862119899

1198601

1198602

119860119898

[[[[[

[

11990911

11990921

sdot sdot sdot

1199091198981

11990912

11990922

sdot sdot sdot

1199091198981

sdot sdot sdot

sdot sdot sdot

sdot sdot sdot

sdot sdot sdot

1199091119899

11990921

sdot sdot sdot

119909119898119899

]]]]]

]

(14)

where 119909119894119895= (1119870)(119909


119896


119870

119894119895) with 119909

119896

119894119895being


119895as


= (119897119896

119894119895 119898119896

119894119895 119906119896

119894119895) and

= (1199081 1199082 119908119899) [40]


= [119903119894119895]119898times119899

119894 = 1 2 119898 119895 = 1 2 119899 (15)

where 119903119894119895= (119886119894119895119888lowast

119895 119887119894119895119888lowast

119895 119888119894119895119888lowast

119895) and 119888

lowast

119895= max

119894119888119894119895are called


119895119888lowast

119895 119886minus

119895119887lowast

119895 119886minus

119895119886lowast

119895) and 119886

minus

119895=





= [V119894119895]119898times119899

= [119903119894119895 (sdot) 119908119894119895]

119894 = 1 2 119898 119895 = 1 2 119899(16)


119894119895


119860+= (V+1 V

+

2 V+

119899)

where V+119895= max119894

V1198941198953 119894 = 1 2 119898 119895 = 1 2 119899


minus

2 Vminus

119899)


V1198941198951 119894 = 1 2 119898 119895 = 1 2 119899

(17)


119894 119889minus



119889+

119894=

119899

sum

119895=1119889V (V119894119895 V

+

119895) = [

[

13

119899

sum

119895=1(V119894119895minus V+119895)2]

]

12

119894 = 1 2 119898

119889minus

119894=

119899

sum

119895=1119889V (V119894119895 V

minus

119895) = [

[

13

119899

sum

119895=1(V119894119895minus Vminus119895)2]

]

12

119894 = 1 2 119898

(18)






minus)


CC119894=

119889minus

119894

119889minus

119894+ 119889+

119894

= (1minus119889+

119894

119889minus

119894+ 119889+

119894

)

for 119894 = 1 2 119898

(19)


119894+ 119889+



119894(119889minus

119894+119889+


alternative








surfacingSlurryseal


overlay Resurfacing

Rutting times times






2+400

2+100





0

2

4

6

8

10

12

Poth

oles

Long

itudi

nal

crac

ks

Tran

sver

secr

acks

Alli

gato

rcr

acki

ng

crac

king

Bloc

k

Rave

ling

Patc

hing

Occ

urre

nce o

f dist

ress



(0+000

ndash3+000

km)










































120582

120572


119885120582

120572=

RS PSR ROS RA100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816


(0170)


(0142)


(0161)


(0229)

100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816

(20)





(MampR) functions


(ROS)

Fog seal

Micro surfacing

Slurry seal

Cape seal

Chip seal

Thin HMA overlay

Resurfacing


Road safety (RS)

Road aesthetics(RA)






1 Fog seal 0755 7















120572119863120582minus

120572


Ranking


0002004006008

01012014016018

02


Stan

dard

ized

rank

ing

inde

x







6 Conclusions









Acknowledgments


References














































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation












surfacingSlurryseal


overlay Resurfacing

Rutting times times






2+400

2+100





0

2

4

6

8

10

12

Poth

oles

Long

itudi

nal

crac

ks

Tran

sver

secr

acks

Alli

gato

rcr

acki

ng

crac

king

Bloc

k

Rave

ling

Patc

hing

Occ

urre

nce o

f dist

ress



(0+000

ndash3+000

km)










































120582

120572


119885120582

120572=

RS PSR ROS RA100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816


(0170)


(0142)


(0161)


(0229)

100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816

(20)





(MampR) functions


(ROS)

Fog seal

Micro surfacing

Slurry seal

Cape seal

Chip seal

Thin HMA overlay

Resurfacing


Road safety (RS)

Road aesthetics(RA)






1 Fog seal 0755 7















120572119863120582minus

120572


Ranking


0002004006008

01012014016018

02


Stan

dard

ized

rank

ing

inde

x







6 Conclusions









Acknowledgments


References














































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation















































120582

120572


119885120582

120572=

RS PSR ROS RA100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816


(0170)


(0142)


(0161)


(0229)

100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816

(20)





(MampR) functions


(ROS)

Fog seal

Micro surfacing

Slurry seal

Cape seal

Chip seal

Thin HMA overlay

Resurfacing


Road safety (RS)

Road aesthetics(RA)






1 Fog seal 0755 7















120572119863120582minus

120572


Ranking


0002004006008

01012014016018

02


Stan

dard

ized

rank

ing

inde

x







6 Conclusions









Acknowledgments


References














































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation












(MampR) functions


(ROS)

Fog seal

Micro surfacing

Slurry seal

Cape seal

Chip seal

Thin HMA overlay

Resurfacing


Road safety (RS)

Road aesthetics(RA)






1 Fog seal 0755 7















120572119863120582minus

120572


Ranking


0002004006008

01012014016018

02


Stan

dard

ized

rank

ing

inde

x







6 Conclusions









Acknowledgments


References














































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation












120572119863120582minus

120572


Ranking


0002004006008

01012014016018

02


Stan

dard

ized

rank

ing

inde

x







6 Conclusions









Acknowledgments


References














































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation













Acknowledgments


References














































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation

























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation









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