Towards sustainable watershed management: a fuzzy

MCDM approach

Ahmad Radmehr1, Mohammad Radmehr

2, Farham Aminsharei

3, Shahab Araghinejad

4

1 Department of Irrigation and Reclamation, Faculty of Agricultural Engineering and

Technology, University college of agriculture and natural resources, Tehran University

2Tehran Regional Water Company, Tehran, Iran

3Departmnt of Science and Department of Nuclear Engineering, Najafabad Branch, Islamic

Azad University, Isfahan, Iran

4Department of Irrigation and Reclamation, Faculty of Agricultural Engineering and

Technology, University College of agriculture and Natural Resources, University of Tehran,

Tehran, Iran

Corresponding author: Farham Aminsharei; email: aminsharei.fa@gmail.com; Tele: (+98)

9376017761;

Abstract

Prioritization of sub-basins available in a basin can be discussed in the form of a multiple

criteria problem. This paper proposes two multi criteria methods, Analytical Hierarchy

Process (AHP) and TOPSIS in fuzzy space to consider some uncertainty in decision making

process with the application of linguistic variables which can be converted to triangular fuzzy

numbers. AHP method is used to determine the structure of decision making process and to

estimate the criteria weights. TOPSIS method is used to rank sub-basins of Taleghan dam

basin. In this research a model is represented in which some vague concepts such as weight

of decision making criteria are expressed in the form of linguistic variables to be converted to

triangular fuzzy numbers. Finally, the sensitivity of model was analyzed by changing the

weight of decision making criteria and providing the ranking scenarios. Results have been

shown that the subbasin 3 has achieved the first ranking. The obtained results can be a good

strategy for qualitative and environmental management in Taleghan dam basin and the other

water supply basin.

Keywords: Environmental Management, Multi Criteria Decision Making, Analytical

Hierarchy Process, Fuzzy TOPSIS.

1. INTRODUCTION

In recent years, the water crisis has appeared the importance of water supply in Tehran city.

According to statistics of 2006, the number of people was 13.41 million that will reach to 18

million people in 2026 in Tehran province. Hence, it is estimated that the water consumption

level with its considerable growth will be equivalent to 1982 mcm/year in 2026. On the other

hand, development of industry and agriculture has also lead to an increase in water

consumption where the total water consumption is predicted to attain by 5135 mcm/year in

2026. Preservation of water sources is not only restricted to the quantity problems because

quality change and polluted water sources mean water loss. Thus, protection of water quality

and prevention from any contaminant could solve the water supply problems in Tehran. To

identify the contaminant factors and sources, investigations on environmental and quality

aspects of water resources, as the first step in quality management of watersheds, is essential

in watershed of Tehran.

Some of the problems of real world cases of management can be considered as multi-criteria

analysis problems that include the assessment and selection of resources, strategies, projects,

proposals and policies.

For a stable management of watersheds, collaboration of several proficient consists of social

science, natural science, water resources managers, designers and politicians are required.

The main difference between various parts of expert’s knowledge leads to an unreliable

output. In this regard, application of technology, factors, spatial scenarios and multi criteria

analysis can help to improve the efficiency of a permanent management in a basin (Macleod

et al., 2007).

A multi criteria decision-making (MCDM) methodology, developed to design a long-term

water supply system, was used in the Adour-Garonne Basin of southwestern France

(Cordeiro Netto et al., 1996). The main problem in this research was election of the best

site’s alternatives for building a large reservoir. The problem elements consist of four

decision makers, 13 criteria and 38 alternatives. The ELECTRE III technique was used to

reduce the alternatives options to eight efficient alternatives. Evaluation of this model was

also compared to the reality conditions. According to the results of these researches, such

model can be used as the starting point for detail studies by paying attention to its simple and

logical analysis (Cordeiro Netto et al., 1996).

The application of analytical hierarchy process, specially the combination of this method with

the other methods such as mathematical programming namely linear programming (AHP-

LP), AHP–Integer linear programming (AHP–ILP), AHP–Mix integer linear programming

(AHP–MILP), AHP–Goal programming (AHP–GP), artificial intelligence including the

methods like artificial neural network (AHP-ANN) and genetic algorithm (AHP–GA), quality

function deployment (QFD), SWOT analysis and data envelopment analysis (DEA) methods

in various problems such as Trade, transportation, environmental, military, marketing,

agriculture and industry that carried out by various researchers over the years 1997-2006, was

studied (Ho, 2008). It was concluded that the AHP-GP and AHP-QFD methods are the most

widely used in the combined methods of analytical hierarchy process. Also the application of

AHP method in combination with the other mentioned methods has better results than the

AHP method alone.

Application of TOPSIS method in evaluation of water management scenarios and along with

ranking decision making alternatives was assessed. Performance factors of this system were

determined with spatial and temporal behavior (Srdjevic et al., 2004).

All multi criteria decision making (MCDM) problems in reality are faced with various kinds

of uncertainty. One of these uncertain parameters is the preference of the Decision Makers

(DM), which has an important effect on the results. Fuzzy linguistic quantifiers can be used

to reduce such uncertainty in which this approach is accompanied by stochastic nature.

Hence, a new approach was introduced for the fuzzy-stochastic modeling by one of the

MCDM methods in the Sefidrud watershed (Zarghami et al., 2008).

Using Multi-Criteria decision making analysis in Geographic Information System (GIS)

platform has been studied by various researchers in analyzing natural hazard events and

suitability analysis. The appropriate landfill sites were defined using a fuzzy multi criteria

decision analysis in GIS. This study was divided in two parts: In the first-stage, variables

were determined in GIS and in the second stage, the fuzzy multi criteria decision-making

(FMCDM) was applied to identify the potential waste sites where sensitivity analysis of

results was performed using Monte Carlo simulation (Chang et al., 2008).

The application of fuzzy quantifiers on landuse suitability analysis was studied using ordered

weighted averaging (OWA) method in GIS platform. In this research OWA operator can

produce a wide range of scenarios in relation to landuse suitability analysis with changing the

parameters (Malczeweski, 2006).

In a case study of irrigation planning, implicit and ambiguity of values in objective function

were quantified using membership function. Also, uncertainty over the input system with

stochastic planning in view of fuzzy multi-objective problem was modeled (Raju et al.,

1998). In air quality management model study, transforming imprecise constraints into

precise inclusive constraints that correspond to α-cut levels, a decisive model was produced.

Note that parameters of this model were modeled in a fuzzy-stochastic approach (Liu et al.,

2003). A fuzzy multi-criteria group decision-making model based on weighted Borda scoring

method was investigated for watershed ecological risk management. The results of this study

showed that this model is appropriate and reliable for ecological risk decision process

(Fanghu et al., 2010). A study was conducted on fuzzy adaptive management of social and

ecological carrying capacities for protected areas. In this survey, the fuzzy method was

elected to determine whether a protected area ecosystem is consistent with ecological and

social carrying capacities. The main goal of this study was to propose an appropriate pattern

for decision makers in the management of watershed’s sub basin in view of pollution points

(Prato et al., 2009). In a case study of flood management, a new toolbox is developed in Arc

Gis 9.3 software platform that in this toolbox visual basic programming is used as an

interface for multi criteria analyzing (Radmehr and Araghinejad, 2011).

In this research, analysis of contaminant factors in Taleghan dam basin was conducted. To

follow the management principles in control of contaminant factors, based on the wide

surface of Taleghan dam basin, the scattered elements over this basin, and also its sub basins,

different areas of Taleghan dam watershed was prioritize using fuzzy multi criteria decision-

making method. This method as an efficient tool has not yet been applied in quantitative

studies exclusively. The main goal of this study is to propose an appropriate pattern for

decision makers in management of watershed’s sub basin in view of pollution points.

It should be mentioned that the above subject is proposed in multi criteria decision pattern

considering several criteria that are faced with uncertainty and ambiguity. The AHP, TOPSIS

and triangular fuzzy numbers were used in determination of alternatives weights, in fuzzy

decision system with language expressions, and in uncertainty and final ranking of

alternatives, respectively.

2. MATERIALS AND METHODS

2.1. The study area

In this study the basin of Taleghan dam is considered as a study area to analyze and evaluate

existing pollution (Figure 1). The catchment area of the dam is about 949 square kilometers.

The purpose of dam construction is the use of Shahroud river potential water resources,

irrigated water supply (equal to 278 mcm per year) for Qazvin Province as well as urban

water consumption (tantamount to 150 mcm). The storage capacity of the dam equals to 420

mcm while its useful volume is tantamount to 329 mcm.

2.2. Analytical hierarchy process

Analytical hierarchy process is one of the most efficient techniques of decision making that

was introduced for the first time in 1980 (Saaty, 1980). This method is based on pairwise

comparisons which give the ability of comparing different scenarios. Modeling by using this

method includes the following steps:

Establishing a hierarchical structure for the problem.

Determine the pairwise comparison matrix, calculate the criteria weights and

alternatives.

Check the consistency of system.

After determining the hierarchical structure, pairwise comparison matrix must be completed

based on the decision maker’s points of view. This work is done for the elements of each

level separately. In general, if the number of alternatives and criteria is equal to m and n, then

the pairwise comparison matrix of each alternative is m×m matrix and the pairwise

comparison criteria is n×n matrix. The elements of pairwise comparison matrix are indicated

with ija . In AHP method one of the assumptions is that aij = 1/ aji. Therefore, it is clear that if

i=j , then aij=1 . aij elements are selected based on Table 1(Saaty, 1980).

2.3. Fuzzy TOPSIS method

TOPSIS method is used widely in the ranking of problems in the field of water resource

management (Simonovic and Verma, 2008), economy and environment (Montanari, 2004;

Xuebin, 2009), waste management (Cheng et al., 2003) and project management (Kao et al.,

2006). TOPSIS method is one of the most technical schedules for prioritizing alternatives

through the distance from ideal and anti ideal point. In this method, the best alternative must

have shortest distance from positive ideal solution and farthest distance from negative ideal

solution.

Despite the simplicity concepts in this method, one of the disadvantages is that in this method

uncertainties and ambiguities in decision-making process is not considered because of using

the absolute quantities. In the traditional formulation of this method, the personal judgments

of decision-makers are expressed with absolute quantities. But in many application and

practical cases, because of existing uncertainties in decision-making process, decision-makers

can not apply the ambiguities in decision-making process using absolute quantities. Fuzzy

logic in comparison with the classical mathematics is a powerful tool to solve the problems

relating to the complicated system. With regard to the mentioned issues, the use of fuzzy set

theory in decision-making process is one of the most important applications of this theory in

comparison with the classic set theories.

In fact fuzzy decision-making theory tries to model the ambiguities and uncertainties in

preferences, objectives and limitations of decision making problems.

2.4. Fuzzy TOPSIS algorithm steps to prioritize the alternatives

Fuzzy TOPSIS steps are expressed as follows:

1st step: Selection of Jjnixij ,...,2,1,,...,2,1,~ language variables for alternatives per

decision criteria.

2nd

step: Calculation of normalized weighted fuzzy decision matrix and weighted normalized

values of ijv~ using equations 1 and 2.

(1)

(2)

3rd

step: Determination of the positive ideal solution ( A ) and negative ideal solution ( A ).

Fuzzy positive ideal solution ( AFPIS , ) and Fuzzy negative ideal solution ( AFNIS , ) are

presented using equations 3 and 4.

(3)

(4)

Where,

I is considered as a benefit criteria set while I is defined as a cost criteria set.

4th

step: The calculation of each alternative distance from FPIS and FNIS using equations 5

and 6:

(5)

(6)

.,...,2,1,,...,2,1,~~JjnivV

jnij

iijij wxv ~~

niIivIivvvvA ijj

ijj

i ,...,2,1,minmax~,...,~,~21

Jj ,...,2,1

niIivIivvvvA ijj

ijj

i ,...,2,1,maxmin~,...,~,~21

Jj ,...,2,1

n

j

iijj vvdD1

~,~ Jj ,...,2,1

n

j

iijj vvdD1

~,~ Jj ,...,2,1

5th

step: CCj index is determined for the jth

alternative (equation 7) by revealing

jD and

jD values.

It is clear that whatever each alternative is closer to FPIS and farther from FNIS, the value of

CCj will be a closer to one.

6th

step: prioritization of alternatives based on CCj values.

2.5. Proposed model for prioritizing of sub-basins

In order to prioritization of pollution within the subbasins of Taleghn a combination of

methods including analytical hierarchy process and fuzzy TOPSIS is applied through

following stages:

Data collection and performing the necessary analysis on them.

Determination of appropriate criteria for decision-making process in relation to the

relevant subject.

Using multi-criteria decision-making method (analytical hierarchy process) to

determine the relative weights of selected criteria.

The assessment of the alternatives using fuzzy TOPSIS model and determination the

final prioritization of alternatives.

At the first stage of the current study, alternatives and decision making criteria are defined

and the hierarchical structure is formed in which the first, second and third levels are

belonged to the ultimate goal, decision making criteria and alternatives, respectively. After

finalization of hierarchical structure, weighing of criteria is carried out using the pairwise

comparison matrix. The values of pairwise comparison matrix have been determined based

on Saatie’s Table and the weights of the criteria have been calculated based on geometric

mean values.

In the next step using fuzzy TOPSIS algorithms based on affecting parameters on water

pollutant in Taleghan dam basin, analyzing these factors in each of sub basins and finally

(7)

jj

j

jDD

DCC Jj ,...,2,1

prioritizing the sub basins is done. At this stage, the linguistic variables are applied to assess

the alternatives. Membership functions related to these linguistic expressions is shown in

Figure 2. Also triangular fuzzy numbers associated with the linguistic expressions is

presented in Table 2.

2.6. Developing criteria in the decision-making process

Regarding to the research algorithm (Figure 3), one of the important stages, is recognizing the

pollutant factors in the basin in this stage, conditions and the present situation is studied.

In this study all criteria that are identified as environmental factors in the basin, must be

studied. In fact, main part of pollutant factors are located in the basin, and thus evaluate the

status of basin leading to a reservoir, provide a suitable situation for identifying these

potentials, properly. All studies in this part should be performed in a spatial manner with full

specifications in order to analyze them at the later stages. The factors were studied in the

basin, consisting two main factors: human factors and natural factors. Parameters were

extracted from all effective pollutant factors in the Taleghan basin in order to analysis and

prioritize sub-basins based on studies and various information resources, especially in

environmental studies in the watershed include: Population centers wastewater (rural/urban),

recreational and tourism activities (tourism), agricultural activities including the amount of

agricultural lands, fertilizer and pesticide usage, catchment area, roads and transportation,

activities including kind of industrial units, the amount of sewage and pollutant factors and

the amount of land cover. The sub basins of Taleghan dam basin have been introduced as

decision-making alternatives. The hierarchical structure with criteria and available

alternatives in decision making process is presented in Figure 4. According to Figure 4,

the first level of hierarchical structure presents the goal of decision-making problem, the

second level presents the criteria for prioritizing the alternatives and the third level presents

the alternatives themselves which is in fact Taleghan dam sub-basins.

3. RESULTS AND DISCUSSION

3.1. Calculation the weights of criteria

The criteria weights are calculated using AHP method after determining the hierarchical

structure of the research. The values of pairwise comparison matrix are determined using

Saatie’s Table that the results of these calculations are presented in Table 3. The

inconsistency ratio (IR) for pairwise comparison matrix is determined that shows the

consistency of results. Prioritizing the decision making criteria based on their weights is

presented in Figure 5.

3.2. Evaluation and final ranking of alternatives

At this stage of the decision making process the preferences rate of alternatives are

determined in exchange for each criteria. Fuzzy matrix related to pairwise comparison of

alternatives based on the linguistic variables is presented in Table 4. In this Table A1 to A6

present the alternatives (sub basins of Taleghan dam basin) and C1 to C7 present the decision

making criteria. In the next step, after determining the fuzzy decision matrix, the weighted

fuzzy decision making matrix is calculated using the weights of criteria from AHP method.

The results of weighted fuzzy decision making matrix are shown in Table 5. Table 5 shows

that the elements ijV~

for all values i and j, are normalized positive triangular Fuzzy numbers

and their values are in the closed interval [0,1]. With regard to the mentioned issues for the

benefit criteria, the fuzzy positive ideal solution (FPIS,A*) and the fuzzy negative ideal

solution (FNIS,A-) are defined as 1,1,1~* iv and 0,0,0

~

iV respectively. Also for cost

criteria, the values of FPIS and FNIS are defined as 0,0,0~* iv and 1,1,1~

iV ,

respectively. In this research, regarding the predefined ultimate goal i.e. sub-basins

prioritization from the perspective of environmental management, all criteria except land

cover were considered as benefit criteria and land cover was considered as cost criteria. In

the next step, distance of each alternative from positive and negative ideals i.e. *D and

D values were calculated using equation 5 and 6 which were referred to in fuzzy TOPSIS

algorithm. Afterward, the values of CCj index was computed from *D and D values

through equation 7. Calculations results related to the CCj index for decision making

alternatives are presented in Table 6. The results of the model show that sub-basin No.3 with

CCj index equivalent to 0.271 has been selected as first priority studies in terms of

environmental studies. Final priority of alternatives based on CCj index is demonstrated in

Table 6.

3.3. The sensitivity analysis of the model

The purpose of the model sensitivity analysis is to determine how alternatives are affected by

variation of inputs (weight values of criteria). This analysis makes ensure that the proposed

solution is reliable. This finding is particularly important when the input data are not accurate

enough. From a wider point of view, it can be realized that how the changes in the model

affect the resulting outcomes. In order to perform sensitivity analysis, criteria weight was

displaced. Thereby, according to the decision making criteria (seven criteria) 21

combinations were derived from criteria weights. It should be noted that each of these

compounds were considered as a weighting scenario. The results of the model sensitivity

analysis are presented in Figure 6 and Table 7. It should be noted that the final values

of criteria weights in original state, have been extracted from multi-criteria analysis is

considered in Figure 6 and Table 7. The ccj values are calculated based on different scenarios

of criteria weighting and the results are presented in Table 7. For example, CC26 represents

the scenario that the second and sixth criteria weight is displaced. According to Table 7, in

17th scenario that the fourth and sixth criteria weight has been displaced, A1 alternative has a

highest value equal to 0.272 compared to its initial value, 0.271. In 3rd scenario that the first

and fourth criteria weight has been displaced, A2 alternative has a highest value equal to

0.204 compared to its initial value 0.195 and A3 alternative has a highest value equal to

0.252 compared to its initial value 0.219. In 1st scenario that the first and second criteria

weight has been displaced, A4 alternative has a highest value equal to 0.209 compared to its

initial value 0.181 and A5 alternative has a highest value equal to 0.228 compared to its

initial value 0.217. A6 alternative has a highest value equal to 0.218 compared to its initial

value 0.204 in 14th scenario that the 3rd and sixth criteria weight has been displaced. Also

the least value of ccj for all alternatives was achieved in 6th

scenario that the first and seventh

criteria weight has been displaced. The least values of ccj for A1, A2, A3, A4, A5 and A6

alternatives are equal to 0.195, 0.119, 0.161, 0.141, 0.178 and 0.147, respectively. It is

observed that A1 alternative has acquired the first priority in all scenarios. Also A3

alternative has acquired the second priority in12 scenarios and the 3rd priority in 6 scenarios,

A5 alternative has acquired the 3rd priority in 9 scenarios and the second priority in

10 scenarios, each of A6, A2 and A4 alternatives has acquired the fourth, fifth and sixth

priority in 15 scenarios, respectively.

4. Conclusion

The current study aims to prioritization of sub-basins are in Taleghan basin from the

perspective of environmental management. For this purpose, several criteria are required to be

defined that might be in contradiction with each other and cause confusion through the

decision making process. Thus, decision making necessitate the use of a method considered

ambiguity and uncertainty within the decision making process. In this study, using the

linguistic variables that can be converted to triangular fuzzy numbers, the uncertainty in the

decision making process has been discussed in the form of fuzzy multiple criteria decision

making method. Hence, a model of decision making with regard to the available alternatives

(under study sub basins) was developed based on a defined set of criteria. The presented

model combined the concepts of fuzzy, analytical hierarchy process and fuzzy TOPSIS

algorithm, can help to take into account some vague concepts such as the weight of the

decision making criteria in the form of a multi-criteria decision making issue. Analytical

hierarchy process is applied for determining weights in the decision-making process and

TOPSIS model in fuzzy space is used for the final ranking of alternatives. Finally, the

reliability of the mentioned model was examined using sensitivity analysis. The results of

sensitivity analysis showed that sub-basin 1 has achieved the first priority in all scenarios.

The results indicate that, A3 alternative has the second priority in 12 scenarios and the third

priority in 6 scenarios, A5 alternative has the third priority in 9 scenarios and the second

priority in 10 scenarios, also each of A6, A2 and A4 alternative has the fourth, fifth and sixth

priority in 15 scenarios, respectively. As regards one of the basic principles of environmental

management is informing of priorities, the results of this model can be an appropriate

solution for applying qualitative and environmental management in Taleghan dam basin.

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Figure 1. Study area of Taleghan dam basin

Figure 2. The equivalent membership functions of the linguistic variables

Figure 3. Proposed algorithm in order to prioritize the sub basins of Taleghan dam basin for

environmental management

Figure 4- Hierarchical structure of prioritizing the sub basins of Taleghan dam basin

IndustryIndustry

Waste water Waste water

AgriculturAgricultur

TourismTourism

area of

sub-basin

area of

sub-basin

Access roadsAccess roads

Land coverLand cover

0.4170.417

0.2390.239

0.1570.157

0.0900.090

0.0460.046

0.0300.030

0.0210.021

Figure 5. Prioritizing the decision making criteria

Figure 6- Sensitivity analysis of model for weighting scenarios

Table 1. Numerical quantities of priority in pair-wise comparisons

Preferences Numerical quantities

Extremely Preferred 9

Very Strongly Preferred 7

Strongly Preferred 5

Moderately Preferred 3

Equally Preferred 1

Table 2. linguistic variables and fuzzy numbers

linguistic variables fuzzy numbers

Very low(VL) (0, 0, 0.2)

Low(L) (0, 0.2, 0.4)

Medium(M) (0.2, 0.4, 0.6)

High(H) (0.4, 0.6, 0.8)

Very high(VH) (0.6, 0.8, 1)

Table 3. The results of analytical hierarchical process

C1: industrial activities, C2: Access roads,

C3: wastewater derived from rural population centers, C4: tourism

C5: agricultural activities, C6: the area of the sub-basins, C7: land cover.

λmax: maximum value of eigen vector, CI: consistency index, RI: random index

Table 4. Fuzzy decision making matrix and its equivalent triangular fuzzy numbers

Table 5. The weighted fuzzy decision making matrix

Excellent(E) (0.8, 1, 1)

CR λ max, CI, RI weight criteria

max = 7.871 λ 0.417 C1

0.030 C2

0.1 CI= 0.145 0.239 C3

0.090 C4

RI= 1.32 0.157 C5

0.046 C6

0.021 C7

C1 C2 C3 C4 C5 C6 C7

A1 excellent excellent excellent very high excellent excellent medium

(0.8, 1, 1) (0.8, 1, 1) (0.8, 1, 1) (0.6, 0.8, 1) (0.8, 1, 1) (0.8, 1, 1) (0.2, 0.4, 0.6)

A2 medium very low medium high low low excellent

(0.2, 0.4,

0.6)

(0, 0, 0.2) (0.2, 0.4, 0.6) (0.4, 0.6, 0.8) (0, 0.2, 0.4) (0, 0.2, 0.4) (0.8, 1, 1)

A3 low low very high excellent very high very high very high

(0, 0.2, 0.4) (0, 0.2, 0.4) (0.6, 0.8, 1) (0.8, 1, 1) (0.6, 0.8, 1) (0.6, 0.8, 1) (0.6, 0.8, 1)

A4 very low

high low medium high medium high

(0, 0, 0.2) (0.4, 0.6, 0.8) (0, 0.2, 0.4) (0.2, 0.4, 0.6) (0.4, 0.6, 0.8) (0.2, 0.4, 0.6) (0.4, 0.6, 0.8)

A5 high very high high low medium very low very low

(0.4, 0.6,

0.8)

(0.6, 0.8, 1) (0.4, 0.6, 0.8) (0, 0.2, 0.4) (0.2, 0.4, 0.6) (0, 0, 0.2) (0, 0, 0.2)

A6 very high medium very low very low very low high low

(0.6, 0.8, 1) (0.2, 0.4, 0.6) (0, 0, 0.2) (0, 0, 0.2) (0, 0, 0.2) (0.4, 0.6, 0.8) (0, 0.2, 0.4)

criteria weights

from AHP method

0.417 0.030 0.239 0.090 0.157 0.046 0.021

Table 6. The final priority of alternatives based on CCj index

Table 7. The sensitivity analysis of the model

weighting

scenarios criteria weights CCJ values for decision-making alternatives

w1 w2 w3 w4 w5 w6 w7 A1 A2 A3 A4 A5 A6

original state 0.417 0.03 0.239 0.09 0.157 0.046 0.021 0.271 0.195 0.219 0.181 0.217 0.204

1= CC12 0.03 0.417 0.239 0.09 0.157 0.046 0.021 0.271 0.178 0.219 0.209 0.228 0.182

2= CC13 0.239 0.03 0.417 0.09 0.157 0.046 0.021 0.271 0.195 0.234 0.184 0.217 0.186

3= CC14 0.09 0.03 0.239 0.417 0.157 0.046 0.021 0.265 0.204 0.252 0.195 0.200 0.171

4= CC15 0.157 0.03 0.239 0.09 0.417 0.046 0.021 0.271 0.189 0.240 0.199 0.210 0.178

5= CC16 0.046 0.03 0.239 0.09 0.157 0.417 0.021 0.271 0.186 0.249 0.197 0.190 0.193

6= CC17 0.021 0.03 0.239 0.09 0.157 0.046 0.417 0.195 0.119 0.161 0.141 0.178 0.147

7= CC23 0.417 0.239 0.03 0.09 0.157 0.046 0.021 0.271 0.186 0.203 0.192 0.223 0.213

8= CC24 0.417 0.09 0.239 0.03 0.157 0.046 0.021 0.272 0.191 0.213 0.182 0.222 0.206

9= CC25 0.417 0.157 0.239 0.09 0.03 0.046 0.021 0.271 0.193 0.209 0.181 0.224 0.210

10= CC26 0.417 0.046 0.239 0.09 0.157 0.03 0.021 0.271 0.195 0.218 0.181 0.219 0.203

11= CC27 0.417 0.021 0.239 0.09 0.157 0.046 0.03 0.269 0.194 0.218 0.179 0.216 0.203

12= CC34 0.417 0.03 0.09 0.239 0.157 0.046 0.021 0.268 0.199 0.222 0.184 0.209 0.204

C1 C2 C3 C4 C5 C6 C7

A1 (0.334,0.417,0.417) (0.024,0.03,0.03) (0.191,0.239,0.239) (0.054,0.072,0.09) (0.126,0.157,0.157) (0.037,0.046,0.046) (0.004,0.008,0.013)

A2 (0.083,0.167,0.25) (0,0,0.006) (0.048,0.096,0.143) (0.036,0.054,0.072) (0,0.031,0.063) (0,0.009,0.018) (0.017,0.021,0.021)

A3 (0,0.083,0.167) (0,0.006,0.012) (0.143,0.191,0.239) (0.072,0.09,0.09) (0.094,0.126,0.157) (0.028,0.037,0.046) (0.013,0.017,0.021)

A4 (0,0,0.083) (0.012,0.018,0.024) (0,0.048,0.096) (0.018,0.036,0.054) (0.063,0.094,0.126) (0.009,0.018,0.028) (0.008,0.013,0.017)

A5 (0.167,0.25,0.334) (0.018,0.024,0.03) (0.096,0.143,0.191) (0,0.018,0.036) (0.031,0.063,0.094) (0,0,0.009) (0,0,0.004)

A6 (0.25,0.334,0.417) (0.006,0.012,0.018) (0,0,0.048) (0,0,0.018) (0,0,0.031) (0.018,0.028,0.037) (0,0.004,0.008)

ideal

(+) )1,1,1(~*

1 v

)1,1,1(~*

2 v

)1,1,1(~*

3 v

)1,1,1(~*

4 v

)1,1,1(~*

5 v

)1,1,1(~*

6 v

)0,0,0(~*

7 v

ideal

(-) )0,0,0(~

1 v

)0,0,0(~2 v

)0,0,0(~

3 v

)0,0,0(~4 v

)0,0,0(~

5 v

)0,0,0(~6 v

)1,1,1(~

7 v

The final ranking of the options jCC

jD *

jD Alternatives

1 0.271 1.899 5.109 A1

5 0.195 1.376 5.665 A2

2 0.219 1.544 5.494 A3

6 0.181 1.272 5.773 A4

3 0.217 1.527 5.505 A5

4 0.204 1.434 5.604 A6

13= CC35 0.417 0.03 0.157 0.09 0.239 0.046 0.021 0.271 0.193 0.219 0.185 0.215 0.204

14= CC36 0.417 0.03 0.046 0.09 0.157 0.239 0.021 0.271 0.190 0.219 0.185 0.203 0.218

15= CC37 0.417 0.03 0.021 0.09 0.157 0.046 0.239 0.229 0.153 0.169 0.154 0.196 0.194

16= CC45 0.417 0.03 0.239 0.157 0.09 0.046 0.021 0.270 0.199 0.221 0.179 0.215 0.204

17= CC46 0.417 0.03 0.239 0.046 0.157 0.09 0.021 0.272 0.193 0.219 0.181 0.216 0.207

18= CC47 0.417 0.03 0.239 0.021 0.157 0.046 0.09 0.259 0.180 0.202 0.171 0.214 0.201

19= CC56 0.417 0.03 0.239 0.09 0.046 0.157 0.021 0.271 0.195 0.219 0.178 0.212 0.212

20= CC57 0.417 0.03 0.239 0.09 0.021 0.046 0.157 0.245 0.173 0.188 0.157 0.207 0.198