Towards sustainable watershed management: a fuzzy MCDM approach

Towards sustainable watershed management: a fuzzy MCDM approach

Ahmad Radmehr¹, Mohammad Radmehr², Farham Aminsharei³, Shahab Araghinejad⁴

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 analyticalhierarchy 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 witha_ij. In AHP method one of the assumptions is that aij = 1/ aji. Therefore, it is clear that if i=j , then ^aij=1. a_ij 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:

1^st step: Selection of



~^xij,ⁱ1,2,...,ⁿ,^j1,2,...,^J



language variables for alternatives per decision criteria.

2^nd step: Calculation of normalized weighted fuzzy decision matrix and weighted normalized values of v~_ij using equations 1 and 2.

( )1

( )2 3^rd step: Determination of the positive ideal solution (A^) and negative ideal solution (A^).

Fuzzy positive ideal solution (FPIS,A^) and Fuzzy negative ideal solution (FNIS,A^) 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.

4^th step: The calculation of each alternative distance from FPIS and FNIS using equations 5 and 6:

( )5

( )6

 

^{~ , 1,2,..., , 1,2,..., .}

~ v i n j J

V  ij n_j  

i ij

ij x w

v ~ 

~



^{v v v}



^{v i I v i I i n}

A _ij

ij j

i maxj min , 1,2,...,

,...,~ ,~

~

2

1 







    



 ^{  }

 j1,2,...,J



^{v v v}



^{v i I v i I i n}

A _ij

ij j

i minj max , 1,2,...,

,...,~ ,~

~

2

1 







    



 ^{  }

 j1,2,...,J

 







  ⁿ

j

i ij

j d v v

D

1

,~

~ j1,2,...,J

 







  ⁿ

j

i ij

j d v v

D

1

,~

~ _{j1,2,...,J}

5^th step: CCj index is determined for the j^th alternative (equation 7) by revealing D_j^and



Dj 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.

6^th 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







 

j j

j

j D D

CC D j1,2,...,J

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 V~_ij

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 ^~v_i^* 

 

^1,1,1 and V~_i^ 



0,0,0



respectively. Also for cost criteria, the values of FPIS and FNIS are defined as ~v_i^*



0,0,0



and V~_i^ 

 

1,1,1, 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 6^th 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.

5. References

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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

Industry Industry Waste water Waste water

Agricultur Agricultur

Tourism Tourism area of sub-basin

area of sub-basin Access roads Access roads Land cover Land cover

0.417 0.417 0.239

0.239 0.157

0.157 0.090 0.090 0.046 0.046 0.030

0.030 0.021 0.021

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)

λ max, CI, RI CR weight

criteria

max = 7.871 0.417 λ

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 CCj



Dj

*

Dj

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