analytical hierarchy process using fuzzy inference technique for real time route guidance system

84 IEEE TRANSACTIONS ON INTELLIGENT TRANSPORTATION SYSTEMS, VOL. 15, NO. 1, FEBRUARY 2014

Analytical Hierarchy Process Using Fuzzy InferenceTechnique for Real-Time Route Guidance System

Caixia Li, Sreenatha Gopalarao Anavatti, and Tapabrata Ray

Abstract—This paper focuses on an optimum route search func-tion in the in-vehicle routing guidance system. For a dynamicroute guidance system (DRGS), it should provide dynamic routingadvice based on real-time traffic information and traffic condi-tions, such as congestion and roadwork. However, considering allthese situations in traditional methods makes it very difficult toidentify a valid mathematical model. To realize the DRGS, thispaper proposes the analytical hierarchy process (AHP) using afuzzy inference technique based on the real-time traffic informa-tion. This AHP–FUZZY approach is a multicriterion combinationsystem. The nature of the AHP–FUZZY approach is a pairwisecomparison, which is expressed by the fuzzy inference techniques,to achieve the weights of the attributes. The hierarchy structure ofthe AHP–FUZZY approach can greatly simplify the definition ofa decision strategy and explicitly represent the multiple criteria,and the fuzzy inference technique can handle the vagueness anduncertainty of the attributes and adaptively generate the weightsfor the system. Based on the AHP–FUZZY approach, a simulationsystem is implemented in the route guidance system, and theprocess is analyzed.

Index Terms—Analytical hierarchy process (AHP), fuzzyinference technique, real-time route guidance.

I. INTRODUCTION

THE ROUTE guidance system is a routing system thatprovides an optimum route to drivers based on a cost

function and a route solution. The cost function is related tothe travel time (TT), distance, or the cost of a road segment,etc. Based on the cost function, the route choice mechanismcan provide the optimum route for drivers. The route choicemechanism is the key technique of vehicle navigation systemsproviding path-planning strategy for travelers. Defining suitablemathematical models to represent the route choice mechanismin traditional methods uses numerical techniques where per-ceived traffic attributes are treated as crisp inputs, such as TTs.However, much of human reasoning is based on imprecise,vague, and subjective values. Thus, the traditional methodsignore the presence of vagueness and ambiguity in drivers’perception, making them difficult to be valid mathematicalmodels.

From the human reasoning perspectives, the fuzzy logicand the developed fuzzy model techniques show great advan-tage to model human decision-making process over traditionalmethods. Teodorovic and Kikuchi [1] first proposed the fuzzy

Manuscript received October 4, 2012; revised April 8, 2013 and July 1, 2013;accepted July 3, 2013. Date of publication July 25, 2013; date of current versionJanuary 31, 2014.

The authors are with the University of New South Wales, Canberra,ACT 2612 Australia (e-mail: [email protected]; [email protected]; [email protected]).

Digital Object Identifier 10.1109/TITS.2013.2272579

logic method in route selection. The drivers’ perceived TTs aretreated as fuzzy numbers, and route choices are given by anapproximate reasoning model and fuzzy inference. This modelconsists of rules indicating the degree of preference of eachroute. However, this model only considers TT attributes, whichis also difficult when generalized to multiple routes. Teodorovicand Kalic [2] proposed a route choice model using fuzzy logicin air transportation. This approach, other than TT, considersmore attributes, such as travel cost, flight frequency, and thenumber of stopovers. However, it is limited to two possibleroutes.

Lotan and Koutsopoulos [3] also proposed a modeling routechoice framework based on fuzzy set theory and approximatereasoning. This approach extended the perceived traffic at-tributes used in the route choice mechanism. However, thisapproach work for particular origin/destination (O/D) pair, andit is also difficult to generalize for different O/D pairs.

Pang et al. [4] proposed a fuzzy–neural approach. The pro-cedures and membership functions of the fuzzy system can beretrieved from the implementation of the neural network. Aspecial learning algorithm is used to learn and adapt itself tothe recent choices of the driver. This approach is not simplyminimization of TT, but more attributes are considered in thismodel. In addition, it can handle more than two feasible routesand apply to any O/D pair with any number of feasible routes. Inparticular, its learning algorithm can also learn from the choiceselection of the driver. However, it has a high requirement ofquality data, and the training procedure is time-consuming.

Yager and Kelman [5] introduced an extension of the an-alytical hierarchy (AHP) approach using ordered weightedaveraging (OWA) operators, suggesting that the capabilities ofAHP as a comprehensive tool for decision-making improvedby integration of the fuzzy linguistic OWA operators. OWA isa kind of a multicriterion aggregation procedure, which wasdeveloped in the context of fuzzy set theory and is composedof two weights: the weights of criterion importance and orderweights. The order weights decide the optimum route choice ofroad network, whereas the AHP proposed by Saaty in 1980 isbased on the additive weighting model. The route choice canbe given by a two-step method. First, the AHP decomposes thedecision problem into a hierarchy of subproblems composedof several criteria, and the importance of weights is associatedwith their criteria. Then, the weights can be aggregated with thecriteria by the weighted combination methods. This approachis of great importance for spatial decision problems that cannotcomplete pairwise comparisons of the alternatives [6], [7].

Boroushaki and Malczewski [8] used a quantifier-guidedOWA combination with AHP by the fuzzy linguistic quantifiers.

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LI et al.: ANALYTICAL HIERARCHY PROCESS USING FUZZY INFERENCE TECHNIQUE 85

Within the AHP–OWA approach, the fuzzy linguistic quantifierhas the capability of capturing qualitative information which thedecision-maker may discern the relationship between the differ-ent evaluation criteria. Although this fuzzy linguistic quantifiercan enhance the ordered weighted averaging process, due to thevagueness and uncertainty of traffic attributes and route deci-sions, a crisp pairwise comparison of AHP cannot capture thevagueness of traffic attributes. However, it suggests a systematicfuzzy logic inference technique that can be introduced into theAHP structure to compensate for the deficiency of AHP.

Arslan [9] proposed using a fuzzy technique and an ana-lytical hierarchy process (AHP–FUZZY) to handle public as-sessments on transportation projects. This approach can captureessential subjective preferences to pairwise among alternativesby AHP. However, this approach can only respond to currentO/D pairs, but it cannot react to real-time traffic information togenerate a new route.

Thus, this paper introduces the fuzzy logic to improve thequantifying process of the AHP approach. In addition, theaforementioned approaches are mainly based on provision ofO/D pairs’ routes without considering heavy traffic congestionof some road segments, and the optimum route given by thecomparison of the O/D pairs is similar. This paper considersboth the traffic density of road segments of each intersectionand the overall cost of O/D pairs to generate an entirely differentroute, which is of great importance to the extension of routechoice problems. Numerical simulation results are provided toshow the adaptiveness of the route guidance system.

This paper is outlined as follows. Section II gives a descrip-tion on the AHP approach, a fuzzy inference technique, and theprocess of the AHP–FUZZY approach. Section III describesa route selection process based on some important traffic at-tributes and focuses on the implementation procedures applyingthe AHP–FUZZY approach in the real-time route guidance sys-tem. To demonstrate the process of the AHP–FUZZY approach,an implementation of the simulation and the results analysisare presented in Section IV based on Sydney traffic data. Someconclusions are given in Section V.

II. METHODOLOGY

A. AHP Approach

The AHP approach is a flexible but well-structured method-ology to analyze and solve complex decision problems bystructuring them into a hierarchical framework [10]. It can berealized by three steps: 1) development of the AHP hierar-chy; 2) pairwise comparison of elements of the hierarchicalstructure; and 3) construction of an overall priority rating. Forthe first step of the AHP procedure, the decision problem isdecomposed into a hierarchy, which consists of goal, objectives,attributes and alternatives. The pairwise comparison as thesecond step of the AHP procedure is the basic measurementmode employed in the AHP procedures, which can greatlyreduce the conceptual complexity of a problem since only twocomponents are considered at any given time.

The decision hierarchy tree of the AHP can provide theselection and ranking of alternatives by pairwise comparison

according to related criteria. The pairwise comparison matricesare based on the alternatives A1, . . . , Am, in terms of eachcriteria being considered. A pairwise matrix for an expert i withrespect to criterion k can be denoted as

Aki =

A1...

Am

A1 . . . Am⎡⎢⎣ ak, i11 · · · ak, i1m...

. . ....

ak, im1 · · · ak, imm

⎤⎥⎦ .

(1)

Each aij denotes the strengths of preferences that the userbelieve alternative i over alternative j.

Each pairwise matrix in the form of m×m, whose elementsare a′ij’s, is a square positive reciprocal matrix

aij = 1/aji and aii = 1 ∀ i, j = 1, . . . ,m. (2)

Therefore, the ratio either under or above the principal di-agonal of the matrix are enough to complete the matrix bytaking the reciprocals of the given elements. Each aij could beregarded as an estimate of the weight of the alternative i, i.e.,wi, to alternative j, i.e., wj , as follows:

aij = wi/wj . (3)

Then

wi = aijwj . (4)

After the pairwise comparison matrix is obtained, the nextstep is to summarize preferences so that each element can beassigned a relative importance. It can be achieved by com-puting the weights and priorities, w = [w1, w2, . . . , wp] for pobjectives and w(q) = [w1(q), w2(q), . . . , wI(q)] for attributesassociated with the qth objective.

The weights can be achieved by normalizing the eigenvec-tor with respect to the maximum eigenvalue of the pairwisecomparison matrix. The normalized eigenvector consists of aniterative process; first matrix A is calculated by normalizing thecolumns of A, i.e.,

A =[a∗qt

]p×p

(5)

where a∗qt = aqt/∑p

q=1 aqt, for all t = 1, 2, . . . , n.The vector of w can be given by

wq = a∗qt(z) ∀ q = 1, 2, . . . , p. (6)

By the simple rule, the attribute weights can be calculated asfollows:

a∗kh(q) = akh(q)

/l∑

k=1

akh(q) ∀ h = 1, 2, . . . , l (7)

wk(q) = a∗kh(q) ∀ k = 1, 2, . . . l. (8)

Finally, the weights can be given by aggregating the relativeweights of objectives and attribute levels, which can be done bya sequence of multiplication of the matrices of relative weightsat each level of hierarchy. The global weights of each criterionwg

j are calculated as follows:

wgj = wq × wk(q). (9)


Fig. 1. Hierarchical structure of the AHP–FUZZY system.

For the overall evaluation results, Ri of the ith alternative iscalculated as follows:

Ri =

n∑j=1

wgjxij (10)

where xij is associated with a set of standardized criterionvalues, i.e., X = [xij ]m×n, for xij ∈ [0, 1], j = 1, 2, . . . , n.

B. Fuzzy Approach

A fuzzy logic system [11] is a process of mapping an inputspace onto an output space using membership functions andlinguistically specified rules. The process of fuzzy inference in-volves membership functions, logical operations, and IF–THEN

rules. In terms of the AHP approach, the estimation of pairwisecomparison depends on subjective perception or experience ofrelative significance of factors. However, the decision-makercannot determine the relative significant weights with anycertainty between any certain values, such as between scalesof 1 to 9. They can only linguistically describe the factorsA method that can determine weights of pairwise comparisoncorresponding to the degree of importance described by thedecision-maker will be greatly useful. Therefore, fuzzy logictheory representing the inference procedure explicitly by aset of fuzzy IF–THEN rules, which can offer a high degreeof transparency into the system being modeled and can dealwith the ambiguity of the judgment process, can compensatethe disadvantage of the AHP approach. With the inputs andoutput defined, it needs to specify a set of rules to define themodel. The rules of approximate reasoning, which can be usedto describe the route choice, are IF–THEN rules. After the inputsare fuzzified and the degree of each part of the antecedentis satisfied for each rule, the logical operations can help thelogical verbal rules. Finally, the defuzzification process canhelp resolve the output value from the set.

C. AHP–FUZZY Model

An AHP—FUZZY model is proposed in this paper, whichuses a FUZZY model to replace the crisp ratios to presentthe weights of pairwise comparison and to distinguish therelative significance of all factors. In the proposed model, athree-level hierarchical structure is constructed to present the

relationship between a module and a component, as shownin Fig. 1. The AHP–FUZZY structure also consists of goal,objectives, attributes, and alternatives. To adaptively realize theroute guidance system for the whole day, this AHP–FUZZYmodel employs a two-step system. For the first step, it isused to adaptively choose route planning objectives based ontraffic density; for the second step, it generates the weights ofattributes considering both the overall cost of O/D pairs andtraffic on road segments of each intersection. Thus, the spatialdecision problem here involves a set of geographically definedalternatives and a set of evaluation criteria and its associatedweights.

Consider directed graph �G = (V,E) with origin point o ∈ Vand destination d ∈ V . “A” denotes the set of all acyclic routesfrom the origin point o to destination point d on �G = (V,E).For each road segment of the road network, e ∈ E criteria aredefined; then, the multicriterion structure is imposed on the roadnetwork.

As aforementioned, the purpose of this paper is to givethe route decision with the least cost, considering both thetraffic density of road segments of each intersection and theoverall cost of O/D pairs. Suppose that there are a set of malternatives, i.e., m adjacency road segments for each node,which can be denoted by Ai for i = 1, 2, . . . ,m. The al-ternatives are to be evaluated by a set of p objectives Oq ,where q = 1, 2, . . . , p. The objectives are measured in termsof the underlying attributes. Thus, a set of n attributes as-sociated with the p objectives can be denoted by Cj , wherej = 1, 2, . . . , n, whereas a subset of attributes associated withthe qth objective is denoted by Ck(q) for k = 1, 2, . . . , l, l ≤ n.There are two sets of weights, i.e., w = [w1, w2, . . . , wp] andw(q) = [w1(q), w2(q), . . . , wI(q)], and they are assigned to theobjectives and attributes, respectively. The weights have thefollowing properties: wq ∈ [0, 1],

∑pq=1 wq = 1, and wk(q) ∈

[0, 1],∑I

k=1 wk(q) = 1. Based on the basic knowledge ofthe AHP approach, the fuzzy logic approach is employed toimprove its performance. For the weights of the objectives andweights, they are no longer constant values but will be decidedby the fuzzy logic rules. Combining with the given weights,the global weights of each criterion wg

j are calculated as wgj =

wq × wk(q), whereas the performance of alternatives Ai withrespect to attributes Cj represented by a set of standardizedcriterion values X = [xij ]m×n for xij ∈ [0, 1], j = 1, 2, . . . , n.The final evaluation results of the ith alternative can be also


TABLE IDEFINITION AND NORMALIZATION OF THE ROUTE CHOICE CRITERIA

calculated as Ri =∑n

j=1 wgjxij , where xij is associated with

the standardized attribute value.

III. IMPLEMENTATION OF AHP–FUZZY APPROACH

The framework of the AHP–FUZZY model can be dividedinto four parts: 1) the construction of a hierarchical structure, asshown in Fig. 1; 2) the implementation of the AHP; 3) the fuzzyarithmetic operation; and 4) the establishment of the priority ofrelative importance.

A. Traffic Attributes

Traditionally, the movements of vehicles are considered asisolated moving units in the route guidance system. However, acar driving on the road is influenced by the whole road network,including static and dynamic information. Van Vuren and VanVliet [8] assumed that distance or time minimization is theonly criterion for drivers’ route choice. Further study done byBovy and Stern [9] showed that more factors could influenceroute choice, such as TT, travel distance (TD), width of theroad, delays, road safety, traffic density, etc. Generally, distanceand TT are usually considered as the main factors to decidethe route selection in current onboard route guidance systemusually inducing the shortest distance or the least time routebased on the road distance information or history traffic flowinformation. However, the route guidance system based on theshortest route without considering traffic conditions and trafficcongestion, can easily cause traffic congestion, energy waste,and environmental pollution.

In this paper, we focus on the travelers whose purpose oftravel is working. For workers, they always want to get to theirdestination with the least cost, such as with the shortest distanceor at the least time. In this paper, distance and TT are alsoconsidered. When workers travel on nonpeak hours, the shortestdistance or the least time paths are more favorable. However,when workers make a route choice during peak hours, they alsowant to get to their destination with less time delay and lesscongestion, which are all related to traffic density on the route.Thus, the objective attributes considered in this paper mainlyinclude three attributes, i.e., TD, TT, and traffic density, andthe weights of objective attributes are also decided by trafficdensity and volume delays (VYs). The focus of this paper ison the route choice to reduce traffic congestion on the roadsand enhance travel efficiency of drivers. Thus, TD, TT, andtravel density (TS) are the three main criteria considered in thisroute guidance system for k routes given by the route searchalgorithm. The definition and normalization of route choicecriteria are shown in Table I.

Fig. 2. Membership functions of linguistic variables.

B. Fuzzy Rules for Pairwise Comparison

In the pairwise comparison matrices, the crisp ratio of aijare replaced by fuzzy numbers with its membership function,such as that shown in Fig. 2. The fuzzy number representsimportance on linguistic variables. The arithmetic of triangularfuzzy numbers is decided by the degree of confidence level.

In this AHP–FUZZY model, a triangular membership func-tion is used. As to membership functions, it can change theirintervals to modify the membership functions, such as thetriplet fuzzy model (al, am, au), whose membership functionμ(x) is defined as follows:

μA(x) =

⎧⎪⎨⎪⎩0, x < al(x− al)/(am − al), al ≤ x ≤ am(au − x)/(au − am), am ≤ x ≤ au0, x > au.

(11)

It can use the interval of confidence at a given level of con-fidence coefficient β to change the intervals of the membershipfunction, and the triangular fuzzy number Aβ has the followingcharacteristics:

∀β ∈ [0, 1]

Aβ=[aβl , a

βu

]=[(am−al)∗β+al,−(au−am)∗β+au] . (12)

Thus, the intervals of the membership functions can bechanged by various β levels (0 < β ≤ 1).

As in Section II, this model uses a fuzzy model to replacethe crisp ratios to present the weights of pairwise comparisonand to distinguish the relative significance of all factors. Thereare two weights that are to be determined: the weights ofobjective attributes and the weights of alternative attributes.To determine these two weights, this AHP–FUZZY modelemploys a two-step system. For the first step, it presents theweights of objectives based on traffic density; for the secondstep, it generates the weights of attributes considering both the


TABLE IIFIRST-STEP FUZZY (IF–THEN) RULES FOR THE WEIGHTS

OF OBJECTIVE ATTRIBUTES

overall cost of O/D pairs and traffic on road segments of eachintersection.

For the first-step rule, the weights of the objectives are deter-mined by the traffic density and VYs. Thus, traffic density andVYs of fuzzy rules consist of the antecedent and consequentof fuzzy rules that are composed of objective attributes. Thelinguistic descriptions of fuzzy inputs are labeled as “muchmore” (MM), “more” (ME), “medium” (M), “less” (L) and“much less” (ML), and the fuzzy outputs are labeled as “high”(H), “medium” (M), and “low” (L). The weights of the objectiveattributes are determined by the first-step rule, as shown inTable II. The IF–THEN rule can be described by the antecedentand consequent, such as, if TS is much less (ML), then theweight of traffic distance is high (H).

Pairwise comparisons are the key technology of the AHPapproach, which can be implemented by comparing threetraffic attributes: TD, TT and traffic congestion for differ-ent routes based on a fuzzy rule system. As to the valueof the objective weights, it can be generated by the fuzzymembership function and by the defuzzification process. Forthe criterion weight wk(q), it is generated by the secondfuzzy rule.

For the second step, it generates the weights of attributesconsidering both the overall cost between current origin anddestination pairs Ctotal and traffic cost on current road segmentsCsegment of each intersection, which decides which route willbe favorable. Their linguistic importance of antecedent is alsodescribed as “much more” (MM), “more” (ME), “medium”(M), “less” (L), and “much less” (ML), and the consequent isalso described as “high” (H), “medium” (M) and “low” (L).The fuzzy rules for a pairwise comparison of alternatives aredescribed in Table III.

After defining the fuzzy inputs and fuzzy rules, the aggrega-tion of all outputs s is given by

s = maxy∈Y

min (μA(y), μB(y)) (13)

TABLE IIISECOND-STEP FUZZY (IF–THEN) RULES FOR

THE ALTERNATIVES ATTRIBUTES

where y is the universe of discourse, and μA(y) and μB(y) arethe membership functions of the inputs relating to the state ofthe alternatives A and B.

As in most fuzzy systems, a center-of-gravity-based defuzzi-fication is used. The centroid zk corresponding to the alternativek is given by

zk =

N∑i=1

αiOi(k)Si(k)

/ N∑i=1

αiSi(k) (14)

where αi is the degree to which the kth rule is fired, Oi(k)is the centroid of the fuzzy set corresponding to the right-hand-side entry of rule i with respect to alternative k, andSi(k) is the area of this set. (If

∑Ni=1 αiSi(k) = 0, then zk is

equal to 0).Based on the fuzzy rules and the membership functions of

fuzzy sets, the criterion weights wk(q) are generated by thedefuzzification process. The final evaluation results of the ith al-ternative can be also calculated as follows: Ri =

∑nj=1 w

gjxij ,

where xij is associated with the attributes value.


After execution of two step fuzzy rules, the weight objec-tives wq and alternatives wk(q) can be given. Then, the finalevaluation results can be given by the establishment of priorityof relative importance.

C. Consistency Test of Judgment Matrix

To measure the consistency degree in terms of the pairwisecomparison matrix A, the consistency index (CI) can be ob-tained by

CI =λmax − n

n− 1(15)

where n is the number of variables compared and the eigenvalueof λmax is the biggest eigenvalue obtained in terms of theeigenvector. The consistency ratio (CR) of CI is defined asfollows:

CR = CI/RI (16)

where RI is associated with the random CI generated by thepairwise comparison matrix. If CR < 0.1, it indicates a reason-able degree of consistency; otherwise, the CR is not consideredto be suitable, and it needs to be revised through the pairwisecomparison until it reaches the consistency level.

D. Calibration of Fuzzy Rules and Membership Functions

The overall objective of the AHP–FUZZY model is to pro-vide reasonable and plausible route to drivers that can alleviatetraffic congestion. Once the basic framework of rules is es-tablished, the calibration of the model can be further improvefor future choices. To calibrate the model, the actual observedchoices are compared with predicted routes. Since each choicecan be viewed as a collection of rules that contributed to it, thefollowing rating index Ri can be used to generate the rankingof rule i for given L observed choices:

Ri =

∑Ll=1 α

li ∗ δ(l)−

∑Ll=1 α

li ∗ (1− δ(l))∑L

l=1 Fi(l)

for i = 1, . . . , N (17)

where

δ(l) =

{ 1, if correct choice is made for theobservation l

0, otherwise(18)

Fi(l) =

{1, if αl

i > 00, otherwise

(19)

and αli is the degree of ith rule fired for the observed choice l.

Note that if∑L

l=1 Fi(l) = 0, then the ith rule needs to bedeleted from the rule sets.

Therefore, if the right choice is made, each rule i contributesαli to the rating of rule I , and negative αl

i if otherwise. Effectiveaverage (given by dividing by the number of cases in whicheach rule is actually fired to some degree) is used since some“good” rules are rarely fired (such as rules in dealing with

some special events or incidents). Rules with lower weightsindicate some problems, possibly in the rule itself, the relevantmembership functions, or any combination of the above. Thisheuristic method is sequentially executed by picking rules withlow ratings and improving them to make sure some bad rulesare picked.

The implementation process of the AHP–FUZZY system isas follows.

1) For the hierarchical structure of the AHP–FUZZY sys-tem, the goal is to achieve optimum route choices fordrivers. The map layers contain the attributes valuesassigned to road segment, and the standardized criterionvalues are denoted as follows: X = [xij ]m×n for xij ∈[0, 1], j = 1, 2, . . . ,m.

2) In the pairwise comparison matrices, the ratio aij isreplaced by fuzzy numbers. The attributes associated withthe objective are distance, TT, and density, and theirweights can be determined by the first rule system. Thesecond fuzzy-rule-based pairwise comparison system de-termines the road segments’ weight wk(q). Combiningwith the given weights, the global weights of each cri-terion wg

j can be given by wgj = wq × wk(q).

3) The final evaluation cost of the ith alternative can be alsocalculated as follows: Ri =

∑nj=1 w

gjxij , where xij is

associated with the attributes value. After determining allthe cost of routes, optimum routes are given by rankingthe cost of routes.

4) The consistency test of the pairwise matrix is as follows.For each pairwise matrix, it needs to judge if the CRis in the reasonable level; if not, it needs to modifythe pairwise comparison until the consistency level isCR < 0.1.

5) Finally, calibrate the fuzzy rules and membership func-tions to further improve the routes provided to the driver,which are reasonable and plausible.

IV. EMPIRICAL ILLUSTRATION

The case study involves the traffic road network in Sydney.The road network contains 287 nodes and 592 directed edges.This study only considers the weekday traffic conditions be-cause it has similar traffic characters; in addition, this paperonly focuses on the “work” activity, and the travel mode is“car.” Four-week traffic volume data were collected on the mainroads in Sydney in 2005. For the data process, to simulatethe real-time route guidance system, the real-time traffic in-formation and traffic prediction data for the succeeding periodare needed. For the real-time traffic prediction, a hybrid trafficprediction model combining artificial neural networks and theautoregressive integrated moving average method [12] is usedto realize the real-time traffic prediction for the whole periodsof day, which can overcome the extremely overprediction andunderprediction phenomena for some specific periods. First,this paper used the former three-week traffic volume data tobe the training data or historical data to get the real-time trafficprediction model. Second, it uses the fourth-week traffic datato compare with the predicted data. A comparative study showsthat the hybrid traffic prediction model can represent the traffic


Fig. 3. An empirical illustration of the AHP-FUZZY approach.

flow more accurately, and the results gained from this hybridmodel are found to outperform traditional individual methodsmodeling the real urban traffic.

To demonstrate the process of the AHP–FUZZY approach,an example is given in Fig. 3. The objectives are measured interms of three criteria: 1) distance; 2) time; 3) density. Whenthe route selection is implemented, there are a number of routesgiven for selection. In this illustration example, we just considerthe top 3 reasonable routes for analysis.

The demonstration of the process of the AHP-FUZZY ap-proach is described as follows:

1) Firstly, the hierarchical structure of AHP-FUZZY isestablished.

2) This AHP-FUZZY model also has customized character-istic. When the driver makes the route planning, he candetermine the route condition he wants. For example, ifthe driver wants the economic way to get the destination,he can choose less travel distance and travel time tominimize the traffic cost on the road. If the driver wantsto increase the sense of comfort, he can choose less trafficdensity on the road. That is, the driver can choose thedegree of importance of traffic attributes (travel distance,travel time and traffic density). There are three degreesof importance for each attribute for decision-makers tochoose, such as: “less”, “medium” and “more”, and theweights are gained from the degree of importance corre-sponding to attributes. In addition, the traffic conditionsvary intensively from different time periods of day. Forthe peak hours, the traffic cost on this road segment withhigh traffic density is higher than usual during non-peakhours. Thus, based on the average traffic density of routesand volume delays, the weights of attributes can be givenby the first fuzzy rule as shown in Table II. Combingthe weights given by drivers and weights based on theaverage traffic density of routes and volume delays, theweights of attributes can be finally determined. Based on

TABLE IVPAIR-WISE COMPARISON MATRIX OF THE OBJECTIVE ATTRIBUTES

TABLE VPAIR-WISE COMPARISON MATRIX OF

ALTERNATIVES CORRESPONDING TO THE DISTANCE

the three attributes, there are three optimum routes forcase study. Table IV shows the pair-wise comparison ofobjective attributes.

3) After determining the weights of the objective, the secondstep is to get the weights of alternative attributes in termsof the route information. It can also be obtained from thepair-wise comparison of route information based on thesecond as shown in Table III. Table V shows the pair-wisecomparison of alternatives corresponding to distance.

4) Combining with the above weights, the global weightsof each criterion, wg

j can be given by wgj = wq × wk(q).

Finally, the overall priority rating can be given basedon the ranking function: Ri =

∑nj=1 w

gj xij, where xij is

associated with the attributes value. After determining allthe cost of routes, optimum routes are given by rankingthe cost of routes.

In order to validate the AHP-FUZZY model providing op-timum path during the whole time of day, we choose oneof the O/D pairs (from A to B). The objective of this paperto automatically generate optimum routes based on drivers’requirements. For this purpose, this AHP-FUZZY model mustadaptively adjust the attributes weights to get the optimum routefor the whole time periods of day. Fig. 4 shows the weights of


Fig. 4. The weights of traffic attributes change during the whole day.

traffic attributes in terms of least cost route changing during thewhole day. In addition, it also shows that the weights changeless during off-peak hours, while it shows great variabilityduring peak hours. It is suggesting the weights of the trafficattributes change greatly with the traffic flow variation, that is,the route choice changes with traffic flow variation.

In order to further validate the proposed approach, it wascompared with current simulation approaches, such as Multi-Agent Transport Simulation (MATSim) [13], Intelligent Trans-portation System for Urban Mobility (ITSUMO) [14] andMITSIMLab [15] which was developed at MIT IntelligentTransportation Systems Program. The first simulation practice(MATSim) has strength on the planning side. The route plan-ning approach used in MATSim is time-dependent Dijkstraalgorithm, which calculates link travel time from the output ofthe traffic flow simulation. The link travel times are encodedin 15 minutes time bins, thus, they can be used as the weightsof the links in the network graph. It also uses iteration cycleto run the traffic flow simulation with specific plans for theagents, and the uses the planning modules to update plans.Then, the updated plans are applied into traffic flow simulation,etc., until consistency is reached. However, it can not considerfine control measures such as instance and the presence of thetraffic lights in the network. The second simulation (ITSUMO)which focuses on short time control by means of agents incharge of optimization of signal plans just provides basic toolsfor the definition of routes and plans for drivers. In fact,the drivers are no more than particles that have no a prioriroutes and they are re-routed at each intersection according tomacroscopic rules, because the ITSUMO is based on cellularautomata model. Thus, more sophisticated driver behaviorssuch as those based on route planning or en-route decisionare more difficult to implement in ITSUMO. Currently, theITSUMO provides a GUI to define a route for drivers, that is,“floating cars”, but the process is time consuming. The MAISimhas strength on planning without fine control measures, whilethe TISUMO has fine control strategy with basic definitionof routes. For this, Kai Nagel [16] proposed to integrate theMATSim with the ITSUMO to overcome the shortcomings.That is, once the MATSim generates the plans, the ITSUMOread them and executes them with some control carried out. Inthis paper, we only focus on the route selection activity, thus,

Fig. 5. Travel distance comparison during the whole day among MITSIMLab,MATSIM and AHP-FUZZY model.

the route plans generated by the MATSim are compared withAHP-FUZZY approach without considering too much controlmeasures by ITSUMO. The MITSIMLab simulation is a mi-croscopic traffic simulation system which can represent a widerange of traffic management systems and model the responseof drivers to real-time traffic information and control. It canenable the MITSIMLab to simulate the dynamic interaction be-tween traffic management systems and drivers. The route choicemodel implemented in MITSIMLab uses habitual path traveltimes as explanatory variables, which requires an iterative day-to-day perception updating model to improve initial travel timeestimates obtained from planning studies. For each iterationof this process, representing a day, habitual travel times wereupdated as follows:

TT k+1it = λkttkit + (1 − λk)TT k

it (20)

where TT kit and ttkit are the habitual and experienced travel

times on link i, time period t on day k, respectively, and λk

is a weight parameter (0 < λk < 1). In this study, a convexcombinations approach is used to and a constant λk = λ isimplemented.

Comparing with the above mentioned three simulations, theAHP-FUZZY approach is also a time-dependent route planningapproach, which can generate routes for drivers based on realtime traffic information and the routes selected also feed intothe traffic flow simulation for next iteration, and it is alsoa customized model which allows the drivers to define theirroute attributes as the reference for the route selection model.Except the common characteristics, the AHP-FUZZY approachcan greatly simplify the definition of decision strategy andrepresent the multiple criteria explicitly, thus, the model canbe easily extended to deal with a variety of traffic attributes,and the fuzzy inference technique can handle the vagueness anduncertainty of the attributes and adaptively generate the weightsfor the system. In addition, this proposed approach considersboth the traffic density of road segments and the overall costof O/D pairs to generate an entirely different route, which is ofgreat importance to the extension of route choice problems andalleviate traffic congestion.

In order to validate the performance of the AHP-FUZZYmodel, firstly, the travel distance and travel time of a random


Fig. 6. Travel time comparison during the whole day among MITSIMLab,MATSIM and AHP-FUZZY model.

TABLE VIPAIR-WISE COMPARISON MATRIX OF THE OBJECTIVE ATTRIBUTES

route are compared with the MITSIMLab and MATSIM model.The travel distance and travel time comparison results areshown in Figs. 5 and 6. Fig. 6 shows that the MAISIM modelalways choose the least travel time. Because the route plan-ning approach used in MATSim is a time-dependent Dijkstraalgorithm, which calculates link travel time from the outputof the traffic flow simulation. While the route choice modelimplemented in MITSIMLab iteratively uses updated habitualpath travel times and experienced travel time. That is, thedriver usually chooses the habitual routes with the updatedtravel time. Fig. 5 shows that the MITSIMLab model usuallyprovide moderate distance routes which seldom deviate fromthe habitual route. Comparing these three models during peak-hours and non-peak hours, it can be seen that these three modelschoose similar routes during non-peak hours, because there isless traffic during non-peak hours and drivers usually travel byleast cost path. However, during peak hours, the routes providedby these three models are totally different. The MATSIM modelfocuses on the travel time which always get the least traveltime sacrificing distance, while the MITSIMLab model usuallychooses the habitual routes which are usually with less traveldistance sacrificing travel time during peak hours. Comparingwith MATSIM and MITSIMLab model, the routes generated bythe AHP-FUZZY model usually have more distance than thehabitual routes, while have less distance than routes providedby MATSIM model as shown in Table VI.

In order to further investigate the performance of AHP-FUZZY model during peak hours, secondly, the routes arefurther compared as shown in Fig. 7. All of routes are notsuggested to travel on Southern Cross Drive, because there ishigher traffic volume than the average traffic volume on otherroad segments during peak hours as shown in Fig. 8. Althoughthe route provided by the MATSIM has the least travel time,the route takes a part of M4 Western Distributor Freeway as

Fig. 7. Route comparison at 8: 10am among MITSIMLab, MATSIM andAHP-FUZZY model.

Fig. 8. Traffic forecast on Southern Cross Drive.

Fig. 9. Traffic forecast on M4 Western Distributor Freeway.

shown in Fig. 9, which easily cause traffic congestion and it isnot reasonable in practice. It seems the route generated by theMITSIMLab model is most plausible, because it has least traveldistance with less travel time. However, when it gets to theintersection, which has similar traffic as Southern Cross Driveduring peak hours, the route by the AHP-FUZZY approachchanges the route before getting to the intersection to avoidthe traffic congestion. It is reasonable to avoid the high trafficcongestion during peak hours even it may take more traveldistance and travel time.


V. CONCLUSION

In this paper, an AHP–FUZZY approach for route guidancesystem has been proposed in which the fuzzy-rule-based systemare introduced to generate the weights of attributes instead ofthe tradition pairwise comparison. Fuzzy logic theory repre-senting the inference procedure explicitly by a set of fuzzyIF–THEN rules, which can offer a high degree of transparencyinto the system being modeled and deal with the ambiguityof the judgment process, can compensate the disadvantageof the AHP approach. Compared with the traditional routechoice approaches simulated in MATSim and MITSIMLab, thisproposed paper can provide reasonable and plausible optimalroute choice based on the combination of road segments’ costand the overall O/D cost, rather than the route selection among anumber of known routes. Considering the specific road segmentinformation can greatly reduce traffic congestion.

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Caixia Li received the B.E. degree in commu-nication engineering from Changchun University,Changchun, China, and the M.Sc. degree in civil en-gineering and transportation control in South ChinaUniversity of Technology, Guangzhou, China. She iscurrently working toward the Ph.D. degree with theUniversity of New South Wales, Canberra, Australia.

Her research interests include cooperative trans-portation management and route guidance systemsunder provision of real-time traffic information.

Sreenatha Gopalarao Anavatti received the B.E.degree in mechanical engineering from the Univer-sity of Mysore, Mysore, India, and the Ph.D. degreein aerospace engineering from the Indian Institute ofScience, Bangalore, India.

From 1991 to 1997, he was an Assistant Professorwith the Indian Institute of Technology, Mumbai,India. From 1997 to 1998, he was an AssociateProfessor with the Indian Institute of Technology,Mumbai. He is currently a Senior Lecturer with theUniversity of New South Wales, Canberra, Australia.

His research interests include dynamic guidance, active vibration control, andapplications of fuzzy and neural networks for practical applications.

Tapabrata Ray received the B.E. and Ph.D. degreesfrom the Indian Institute of Technology, Kharagpur,India.

From 1996 to 1997, he was a member of the tech-nical staff with the Information Technology Institute,Singapore. From 1997 to 1999, he was a Lecturerwith Singapore Polytechnic, Singapore. From 1991to 2001, he was a Fellow with the Institute of HighPerformance Computing, Singapore. From 2001 to2004, he was a Senior Research Scientist with theNational University of Singapore, Singapore. He is

currently a Senior Lecturer and an Australian Research Council Future Fellowwith the School of Engineering and Information Technology, University ofNew South Wales, Canberra, Australia, where he leads the MultidisciplinaryDesign Optimization Group. His research interests include multiobjective op-timization, constrained optimization, robust design and constrained robust de-sign, dynamic multiobjective optimization, and realistic transportation models.