A Fuzzy Multi Criteria Decision Making Approach for ...

FUZZYSS’15 The 4th International Fuzzy Systems Symposium 5-6 November 2015 İstanbul-Turkey www.fuzzyss.yildiz.edu.tr

PROCEEDINGS viii

A Fuzzy Multi Criteria Decision Making Approach for Evaluating Renewable Energy Sources Yakup Çelikbilek and Fatih Tüysüz 

Abstract—Energy is one of the most important resources for life, and energy resources and energy production have a great importance for both countries and economies. Selecting the suitable and efficient energy resource and energy production method are also crucial within the energy production process. While producing the suitable and efficient energy, potential damages to the environment and the ecological system also have to be taken into consideration. Non-renewable energy sources (NES) have a great impact on the environment and the ecological system. Besides, NES are running out day by day and detriments of NES in the long run will be evident if they are considered with a comprehensive perspective. On the other hand, renewable energy sources (RES) have less impact on the environment and the ecological system without any risk about their extinction. Advantages and disadvantages of RES depend on circumstances. In this study, we aim to analyze the advantages and disadvantages of RES with subjective perspectives using linguistic scales. To this end, fuzzy VIKOR which is a fuzzy multi-criteria decision making approach is proposed and used to evaluate RES.

Keywords: Renewable Energy, Fuzzy Sets, Multi Criteria Decision Making, VIKOR I. INTRODUCTION There is an increasing demand for energy and it is predicted that the world’s average rate of increasing energy demand is 1.8 % per year until 2030 [1]. Despite the increase in demand of energy, there are some problems related to the conventional energy sources, especially for fossil fuels, which are depletion of fossil fuels, carbon emission, price and cost volatility, and environmental effect [2]. In order to overcome these problems, renewable energy sources (RES) are considered to be one the most appropriate alternatives to conventional energy resources. Renewable energy is more environmentally friendly and does not cause pollution [3]. Since renewable energy is produced from natural, recurring and continuous outflow of energy, and does not consume any natural resource and can be naturally replenished, it is also sustainable [4]. Manuscript received July 10, 2015. Y. Çelikbilek, Department of Business Administration, Istanbul University, Istanbul, 34320 Turkey. (corresponding author to provide email: [email protected]). F. Tüysüz, Department of Industrial Engineering, Istanbul University, Istanbul, 34320 Turkey. (e-mail: [email protected]).

Countries need to carefully plan and select the most appropriate energy sources to be able to sustain their social and economic development. Reliance on only one kind of energy source is not possible for most cases and the alternative sources should be considered. RES are an important alternative that should be considered in the energy portfolio of countries. One of the important points in energy planning is to select the most appropriate alternative energy sources. Since the evaluation of RES contains many conflicting criteria to be considered, it can be considered as a typical MCDM problem. Application of multi-criteria decision making methods in energy planning problems enable the clear recognition of the influence of subjective issues on the final ranking of alternatives and also provides insight into priorities and sensitivities of the various actors involved [5]. A detailed literature review related to the application of MCDM methods in the area of energy planning can be found in [6] and [7]. In this study, we present a fuzzy multi-criteria decision making approach for the evaluation of RES. In addition to the practical contribution of our proposed approach to the RES evaluation literature, we believe that this study is significant in another way. We introduce a new fuzzy VIKOR method which can make an important contribution to multi-criteria decision making literature. The organization of the paper is as follows. In section 2, literature review related to the applications of fuzzy VIKOR method is given. In section 3, the developed fuzzy VIKOR method and its algorithmic steps are presented. In section 4, an application of the proposed approach for the evaluation of RES is given. Finally, the results and conclusions are presented. II. LITERATURE REVIEW Amiri, Ayazi, Olfat and Moradi [8] applied a fuzzy VIKOR approach with group decision making process for car parts supplier selection. Authors used linguistic variables which were defined as triangular fuzzy numbers in the study. Kaya and Kahraman [9] proposed an integrated fuzzy AHP– VIKOR approach and applied to rank the watershed district alternatives in İstanbul. They used fuzzy AHP to determine the evaluation criteria and fuzzy VIKOR was applied to the forestation district selection problem. Farsi, Moradi and Jamali [10] rank the cell phone alternatives by using fuzzy VIKOR. They used triangular fuzzy numbers defined as linguistic words in VIKOR

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calculations. Kuo and Liang [11] applied a fuzzy VIKOR approach with interval–valued fuzzy numbers and Euclidean distance to evaluate intercity bus companies. Mohaghar, Fathi, Sasani and Khanmohammadi [12] introduced an integrated fuzzy approach with linear goal programming model and VIKOR method. They determined the weights with linear goal programming and then used fuzzy VIKOR to evaluate the most appropriate strategy. In the study, compromise solutions were obtained as defuzzified values. Ramezaniyan, Kazemi, Jafari and Elahi [13] presented an integrated Fuzzy VIKOR–AHP method which was applied to contractor selection by using triangular fuzzy numbers. Su, Tzeng and Tseng [14] proposed a hybrid fuzzy multi criteria decision making approach by using fuzzy DEMATEL, fuzzy ANP and fuzzy VIKOR. They determined the weights with fuzzy DEMATEL and fuzzy ANP. Fuzzy VIKOR was then used to evaluate the performance of computing applications. They used triangular fuzzy numbers in the application and obtained fuzzy results. Mohaghar, Fathi and Jafarzadeh [15] proposed an integrated approach by using fuzzy VIKOR and assurance region–data envelopment analysis. They applied the proposed approach with triangular fuzzy numbers to evaluate the best supplier alternative for a manufacturing company. Liao and Xu [16] applied VIKOR method with hesitant fuzzy sets. They used hesitant normalized Manhattan distance to calculate the group utility measure, the individual regret measure and the compromise solution. In this study, they evaluated the service quality of domestic airlines with the proposed approach and obtained hesitant fuzzy group utility measures, hesitant fuzzy individual regrets and hesitant fuzzy compromise solutions for alternatives. Bashiri, Mirzaei and Randall [17] presented a hybrid model which uses the fuzzy VIKOR results in genetic algorithm solution. They applied fuzzy VIKOR to evaluate the candidate hub locations in their study. Kim and Chung [18] introduced a fuzzy VIKOR method which uses normalized fuzzy difference calculations in the methodology. The vulnerability of the water supply to climate change was evaluated with the proposed fuzzy VIKOR method. Chang [19] evaluated the hospital service quality with fuzzy VIKOR method. Triangular fuzzy numbers were used and the utility measures, the regret measures and the compromise solutions were obtained with fuzzy numbers at the end of the study. Afful–Dadzie, Nabareseh and Oplatkova [20] proposed a fuzzy VIKOR approach with triangular fuzzy numbers and normalized fuzzy differences. Quality of internet health information was evaluated by the proposed fuzzy VIKOR approach and the results were also obtained as fuzzy numbers in the study. Kavitha and Vijayalakshmi [21] introduced an integrated fuzzy multi objective linear programming model. Fuzzy VIKOR method was applied to rank the alternatives to be used in the fuzzy multi objective linear programming. They applied the proposed approach to a facility location selection problem. In their study, factors were separated as quantitative and qualitative. The qualitative factors were obtained by using fuzzy VIKOR and both of the factors were used in fuzzy multi objective linear

program to evaluate the optimal location. Tadic, Zecevic and Krstic [22] proposed an approach which integrates fuzzy DEMATEL, fuzzy ANP and fuzzy VIKOR methods. They obtained the weights as crisp values which were used in fuzzy VIKOR after the fuzzy DEMATEL and fuzzy ANP process. They used normalized fuzzy difference in the proposed fuzzy VIKOR approach calculations and obtained the utility measures, the regret measures and the compromise solutions as fuzzy numbers. The integrated model was applied to evaluate the city logistic concepts. Zhang, Bouras, Ouzrout and Sekhari [23] proposed an integrated fuzzy AHP–VIKOR method to evaluate product lifecycle management strategies. They used triangular fuzzy numbers for both fuzzy AHP and fuzzy VIKOR calculations. The compromise solutions were obtained by using triangular fuzzy numbers and ranking of the alternatives were obtained as the defuzzified compromise solutions. Adhikary, Roy and Mazumdar [24] applied fuzzy VIKOR and fuzzy TOPSIS to small hydropower projects and compared the results. They did all of the calculations with triangular fuzzy numbers and used defuzzified crisp values to rank the alternatives. Arunachalam, Idapalapati and Subbiah [25] ranked polishing tools with traditional AHP and fuzzy VIKOR. The results for alternatives obtained from these two methods were compared and showed that the results were almost the same. The fuzzy VIKOR results were obtained as triangular fuzzy numbers and rankings were done with defuzzified values. Hacioglu and Dincer [26] used fuzzy AHP–TOPSIS and fuzzy AHP–VIKOR methods to evaluate stock market in emerging economies and compared the results. They ranked the alternatives according to defuzzified values and the same ranking results were obtained from the two hybrid methods. Lee, Jun and Chung [27] proposed an improved group decision making approach combined with fuzzy VIKOR. Dursun [28] applied fuzzy VIKOR to evaluate wastewater treatment alternatives for a case in İstanbul. III. FUZZY VIKOR VIKOR method was firstly introduced by Opricovic [29] for MCDM of complex systems. The method ranks a set of alternatives according to the ideal solution. At the end, compromise solutions are generated between the maximum group utility of the majority and the minimum of the individual regret of the opponents. As mentioned in the previous section, there are some different fuzzy VIKOR approaches in the literature. In this study, we propose a fuzzy VIKOR method is derived as the combination of different fuzzy approaches which are [30], [31], [32] and [33]. Table I presents the notation used in the proposed approach. The computational steps of the proposed fuzzy VIKOR are as follows. Step 1: Determining the alternatives and generating the decision matrix: Let Ai represents the i th alternative among

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m alternatives, w j represents the weight of the j th criterion

 m n

xij among n criteria and X  ~

represents the decision

matrix as given in (1) for an MCDM system. x11 ~ ~ x 21 X   ... ~  x m1

~ x12 ~ x

22

... ~ xm 2

~ x1n   ~ ... x 2 n  ... ...   ... ~ x mn 

Step 4: Calculating the utility measures and the regret measures: The utility measures and the regret measures for each alternative are calculated by using (5) - (6).

...

~ Si 

(1)

Definition the i th alternative

cj

the j th criterion

wj ~ x

the weight of the j th criterion

j 1

 



j th criterion



   



(5)





Qi (1)

Qi ( 2 )

~  S i ( 2 )  min S i (1)  i  v ~ max S min  

Qi ( 3)

~  S i ( 3)  min S i (1)  i  v ~ max S min  



the j th criterion the fuzzy utility measure of the i

th

alternative

the fuzzy regret measure of the i th alternative the fuzzy compromise solution of the i th alternative



the crisp utility measure of the i th alternative th

(6)

Ri

the crisp regret measure of the i

Qi v

the crisp compromise solution of the i th alternative the weight of the maximum group utility



 

~  S i (1)  min S i (1)  i  v ~ max S min  

the weighted fuzzy regret value of the i th alternative for

Si

j 1

ij ( 3)

obtained with the modification of the first normalization part of the CFCS (Converting Fuzzy data into Crisp Scores) method [33]. The calculations are given in (7) to (9).

the normalized fuzzy value of the i th alternative for the

~ Si ~ Ri ~ Qi

j 1

r



alternative for the j th criterion

~ rij



n

rij ( 2 ) ,

Step 5: Calculating the compromise solution: The ~ compromise solution Qi  Qi (1) , Qi ( 2) , Qi (3) values are

the fuzzy value or the performance score of the i th

~ f ij



n

rij (1) ,

 

Ai

ij



n

~   Ri  max ~ rij   max rij (1) , max rij ( 2 ) , max rij (3)  j j j  j 

TABLE I NOTATION Notation

 ~ rij    j 1  n

alternative



~  Ri (1)  min Ri (1)  i ~ max   1  v  Rmin    

 



 



~  Ri ( 2 )  min Ri (1)  i ~ max   1  v  Rmin    

~  Ri ( 3)  min Ri (1)  i ~ max   1  v  Rmin    







~ max S min  max S i ( 3)  min S i (1)

where

 

i

i



(7)

  

    

    

(8)

(9)

and

Step 2: Normalizing the decision matrix: ~ xij  xij (1) , xij ( 2 ) , xij (3)  is a triangular fuzzy number which is

~ max Rmin  max Ri (3)  min Ri (1) . In (7) to (9), v  0,1  R

defined for benefit attribute is normalized as in (2) and the normalized decision matrix is obtained.

is the weight of the maximum group utility and 1  v  is the weight of the individual regret. In the literature, v is mostly taken as 0.5. ~ ~ ~ Step 6: Defuzzification of the S i , Ri and Qi values: The ~ ~ ~ fuzzy values of the S i , Ri and Qi are defuzzified into crisp

  xij (1) xij ( 2 ) xij (3) ~   f ij   , ,  max ( x ) max ( x ) max ( x )  ij ( 3) ij ( 3) ij ( 3)  i i  i 

(2)

Step 3: Determining the ideal solution and calculating the weighted regret matrix: In the normalized decision matrix F, the maximum value is 1. So, the ideal solution for each ~ criterion can be 1  1,1,1 at normalized decision matrix. r are calculated by using (3)Weighted fuzzy regret values ~

i





(3)





~ rij  w j 1  f ij (3) , 1  f ij ( 2) , 1  f ij (1)

i









(10)





(11)





(12)

~ max Qi'(1)   Qi (1)  min Qi (1)  Qmin i   ~ max Qi'( 2 )   Qi ( 2 )  min Qi (1)  Qmin i  

(4).





values ( S i , Ri and Qi ) by CSCF method [33] given in (10) to (16).

ij

~ ~ ~ rij  w j 1  f ij





~ max Qi'( 3)   Qi ( 3)  min Qi (1)  Qmin i  

(4)

~ max  max Qi ( 3)   min Qi (1)  where Qmin i

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i

Qi'(' 1)



Qi'( 2)



1  Qi'( 2)

 Qi'(1)





(13)



(14)

Qi'(' 2)  Qi'(3) 1  Qi'(3)  Qi'( 2)

Qi' ' ' 

   Qi'(' 1)



1  Qi'(' 1) 1  Qi'(' 1)



 Qi'(' 2 ) Qi'(' 2 )  Qi'(' 2 )







~ max Qi  min Qi (1)  Qi' ' ' Qmin i

(C1) criterion as in Table V in order to more focus on the newly introduced fuzzy VIKOR method. TABLE II THE EVALUATION CRITERIA Criteria C1 C2 C3 C4 C5 C6 C7 C8 C9 C10 C11

(15)

(16)

~ ~ S i and Ri values are also defuzzified by applying (10) to (16). Step 7: Ranking the alternatives: S i , Ri and Qi values

Name of the Criteria Sustainability and Accessibility Efficiency/Effectiveness The Variety of the Usage Areas Storability Efficiency of Conveyance Initial Investment Cost Simplicity of the Facility Requirement of Technology Maintenance Requirements Accident Risk and effects Detriments to the Nature and Humans TABLE III RES ALTERNATIVES

are ranked from minimum to maximum respectively and the lists are the utility measure list, the regret measure list and the compromise solution list. The minimum Qi value is the best alternative to compromise between the maximum group utility of the majority and the minimum of the individual regret of the opponents.

Alternative A1 A2 A3 A4 A5

IV. EVALUATING THE RENEWABLE ENERGY SOURCES The proposed fuzzy multi criteria decision approach is applied to evaluate the RES under subjective perspective by using linguistic variables. The RES alternatives and the evaluation criteria were obtained from literature [2], [6], [34], [35], [36], [37], [38] and the experts on RES. 11 criteria which are given in Table II were determined to evaluate the RES alternatives given in Table III. The weights of the criteria were obtained from another ongoing study of the authors. The alternatives are evaluated with fuzzy VIKOR by using the weights given in Table II. The performance score for each alternative with respect to each criterion is required to be able to construct the decision matrix and apply the fuzzy VIKOR method. The decision matrix is obtained with linguistic pairwise comparison scale given in Table IV. These pairwise comparisons between the alternatives for each criterion are evaluated by the 11 experts working on RES. Based on the pairwise evaluations of experts, the relative performance scores of 5 alternatives are obtained by averaging the normalized column values. The results of this stage are directly given for sustainability and accessibility

The Weights 0.033 0.101 0.029 0.119 0.094 0.068 0.088 0.259 0.030 0.120 0.059

Renewable Energy Resource Solar Energy Wind Energy Hydroelectric Energy Geothermal Energy Biomass Energy

TABLE IV LINGUISTIC PAIRWISE COMPARISON SCALE Crisp Value 1 3 5 7 9

Linguistic Term Equally Important (EI) Weakly Important (WI) Important (I) Strongly Important (SI) Absolutely Important (AI)

Fuzzy Number (8,9,9) (6,7,8) (4,5,6) (2,3,4) (1,1,2)

According to all of the pairwise comparison results and the alternative weights, the fuzzy decision matrix given in Table VI is obtained. In Table VI, all of the results are set for benefit according to the evaluation criteria. Fuzzy decision matrix given in Table VI is normalized by using (2) and then weighted fuzzy regret values given in Table VII are calculated by using (3). The fuzzy utility measures and the fuzzy regret measures of the RES alternatives are obtained by using (5)–(6) with the values of Table VII. The fuzzy compromised solutions are calculated by (7) to (9) by taking the v value as 0.5. All ~ ~ ~ of the obtained fuzzy results of S i , Ri and Qi are given in Table VIII.

TABLE V FUZZY PAIRWISE COMPARISONS FOR SUSTAINABILITY AND ACCESSIBILITY OF THE ENERGY SOURCE (C1) A1 A2 A3 A4 A5

A1 (1.000, 1.000, 1.000) (1.817, 2.501, 3.026) (0.833, 0.987, 1.201) (0.324, 0.384, 0.500) (0.727, 0.868, 1.020)

A2 (0.330, 0.400, 0.550) (1.000, 1.000, 1.000) (0.449, 0.523, 0.642) (0.270, 0.315, 0.397) (0.467, 0.577, 0.742)

A3 (0.833, 1.013, 1.201) (1.557, 1.910, 2.226) (1.000, 1.000, 1.000) (1.049, 1.365, 1.619) (1.906, 2.365, 2.942)

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A4 (2.000, 2.605, 3.086) (2.520, 3.173, 3.706) (0.618, 0.732, 0.953) (1.000, 1.000, 1.000) (0.707, 0.918, 1.070)

A5 (0.981, 1.152, 1.375) (1.348, 1.732, 2.140) (0.340, 0.423, 0.525) (0.935, 1.089, 1.414) (1.000, 1.000, 1.000)

The Weights (0.131, 0.181, 0.252) (0.072, 0.098, 0.142) (0.194, 0.271, 0.371) (0.188, 0.265, 0.364) (0.135, 0.185, 0.261)

TABLE VI FUZZY DECISION MATRIX A1 A2 A3 A4 A5

C1 (0.131, 0.181, 0.252) (0.072, 0.098, 0.142) (0.194, 0.271, 0.371) (0.188, 0.265, 0.364) (0.135, 0.185, 0.261)

C2 (0.132, 0.194, 0.276) (0.078, 0.110, 0.164) (0.263, 0.370, 0.516) (0.137, 0.197, 0.280) (0.091, 0.128, 0.192)

C3 (0.221, 0.323, 0.445) (0.106, 0.157, 0.228) (0.170, 0.238, 0.344) (0.059, 0.086, 0.125) (0.141, 0.196, 0.292)

C4 (0.091, 0.137, 0.190) (0.058, 0.084, 0.121) (0.325, 0.453, 0.623) (0.073, 0.098, 0.153) (0.163, 0.228, 0.322)

C5 (0.076, 0.115, 0.156) (0.053, 0.074, 0.110) (0.385, 0.527, 0.706) (0.064, 0.086, 0.134) (0.142, 0.198, 0.282)

A1 A2 A3 A4 A5

C7 (0.099, 0.148, 0.212) (0.242, 0.355, 0.521) (0.177, 0.260, 0.379) (0.067, 0.099, 0.149) (0.095, 0.139, 0.210)

C8 (0.176, 0.270, 0.403) (0.179, 0.276, 0.412) (0.087, 0.132, 0.191) (0.074, 0.111, 0.173) (0.144, 0.212, 0.337)

C9 (0.137, 0.218, 0.318) (0.153, 0.239, 0.361) (0.092, 0.135, 0.213) (0.086, 0.129, 0.196) (0.187, 0.279, 0.436)

C10 (0.206, 0.317, 0.453) (0.146, 0.218, 0.330) (0.104, 0.156, 0.234) (0.078, 0.119, 0.185) (0.130, 0.189, 0.304)

C11 (0.119, 0.193, 0.256) (0.093, 0.142, 0.200) (0.122, 0.176, 0.255) (0.168, 0.240, 0.368) (0.182, 0.249, 0.382)

C6 (0.206, 0.303, 0.428) (0.235, 0.337, 0.472) (0.132, 0.187, 0.269) (0.054, 0.076, 0.110) (0.074, 0.097, 0.146)

TABLE VII WEIGHTED FUZZY REGRET MATRIX A1 A2 A3 A4 A5

C1 (0.011, 0.017, 0.021) (0.020, 0.024, 0.027) (0.000, 0.009, 0.016) (0.001, 0.009, 0.016) (0.010, 0.017, 0.021)

C2 (0.047, 0.063, 0.075) (0.069, 0.079, 0.086) (0.000, 0.029, 0.050) (0.046, 0.062, 0.074) (0.063, 0.076, 0.083)

C3 (0.000, 0.008, 0.015) (0.014, 0.019, 0.022) (0.007, 0.013, 0.018) (0.021, 0.023, 0.025) (0.010, 0.016, 0.020)

C4 (0.083, 0.093, 0.102) (0.096, 0.103, 0.108) (0.000, 0.032, 0.057) (0.090, 0.100, 0.105) (0.057, 0.075, 0.088)

C5 (0.073, 0.079, 0.084) (0.079, 0.084, 0.087) (0.000, 0.024, 0.043) (0.076, 0.083, 0.085) (0.056, 0.068, 0.075)

A1 A2 A3 A4 A5

C7 (0.052, 0.063, 0.071) (0.000, 0.028, 0.047) (0.024, 0.044, 0.058) (0.063, 0.071, 0.077) (0.053, 0.065, 0.072)

C8 (0.006, 0.089, 0.148) (0.000, 0.085, 0.146) (0.139, 0.176, 0.204) (0.150, 0.189, 0.212) (0.047, 0.126, 0.168)

C9 (0.008, 0.015, 0.021) (0.005, 0.014, 0.019) (0.015, 0.021, 0.024) (0.017, 0.021, 0.024) (0.000, 0.011, 0.017)

C10 (0.000, 0.036, 0.065) (0.033, 0.062, 0.081) (0.058, 0.079, 0.092) (0.071, 0.088, 0.099) (0.039, 0.070, 0.086)

C11 (0.019, 0.029, 0.041) (0.028, 0.037, 0.045) (0.020, 0.032, 0.040) (0.002, 0.022, 0.033) (0.000, 0.021, 0.031)

The fuzzy utility measure results, the fuzzy regret measure results and the fuzzy compromise solution results are defuzzified by using (10) to (16). The defuzzified compromise solution results show that the best alternative is solar energy (A1) with the least Qi value of 0.352. With the highest Qi value of 0.807, geothermal energy is the least preferable RES alternative. The defuzzified compromise solution results are given in Table IX. TABLE VIII FUZZY COMPROMISE SOLUTION RESULTS The Maximum The Individual The Compromise

~ 

A1 A2 A3 A4 A5

Group Utility S i (0.305,0.516,0.681) (0.345,0.555,0.702) (0.292,0.500,0.651) (0.589,0.727,0.812) (0.383,0.597,0.718)

~ 

~ 

Regret Ri

(0.083,0.093,0.148) (0.096,0.103,0.146) (0.139,0.176,0.204) (0.150,0.189,0.212) (0.063,0.126,0.168)

Solution Qi

(0.078,0.314,0.659) (0.160,0.386,0.673) (0.253,0.578,0.817) (0.576,0.840,1.000) (0.088,0.503,0.762)

C6 (0.006, 0.024, 0.038) (0.000, 0.019, 0.034) (0.029, 0.041, 0.049) (0.052, 0.057, 0.060) (0.047, 0.054, 0.057)

V. CONCLUSION This study proposed a fuzzy multi criteria decision model combined with fuzzy VIKOR method to evaluate the renewable energy sources. Application results notice that solar energy is the best alternative and the geothermal energy is the least preferable RES alternative. The ranking of the RES alternatives can be an important input for energy planning process and aid the policy makers in deciding which RES alternatives to focus. The presented methodology can also be used for other multi criteria decision making problems. For further research, in addition to the application of the presented methodology for other multi-criteria decision making problems, the application of the proposed fuzzy VIKOR method and also its integration with other fuzzy multi-criteria methods can be a promising area for interested researchers. REFERENCES [1]

TABLE IX RANKING OF THE RES ALTERNATIVES Alternative A1 A2 A5 A3 A4

Renewable Energy Source Solar Energy Wind Energy Biomass Energy Hydroelectric Energy Geothermal Energy

Qi 0.352 0.408 0.482 0.559 0.807

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