A bi-objective score-variance based linear assignment method for group decision making with hesitant fuzzy linguistic term sets
Abstract
Decision makers usually prefer to express their preferences by linguistic variables. Classic fuzzy sets allowed expressing these preferences using a single linguistic value. Considering inevitable hesitancy of decision makers, hesitant fuzzy linguistic term sets allowed them to express individual evaluation using several linguistic values. Therefore, these sets improve the ability of humans to determine believes using their own language. Considering this feature, in this paper a method upon linear assignment method is proposed to solve group decision making problems using this kind of information, when criteria weights are known or unknown. The performance of the proposed method is illustrated in a numerical example and the results are compared with other methods to delineate the models efficiency. Following a logical and well-known mathematical logic along with simplicity of execution are the main advantages of the proposed method.
Keyword : linguistic variables, hesitant fuzzy linguistic term sets, multi-criteria group decision making, linear assignment method, National Cartographic Center
How to Cite
Razavi Hajiagha, S. H., Shahbazi, M., Amoozad Mahdiraji, H., & Panahian, H. (2018). A bi-objective score-variance based linear assignment method for group decision making with hesitant fuzzy linguistic term sets. Technological and Economic Development of Economy, 24(3), 1125-1148. https://doi.org/10.3846/20294913.2016.1275878
This work is licensed under a Creative Commons Attribution 4.0 International License.
References
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Baykasoğlu, A.; Subulan, K.; Karaslan, F. S. 2016. A new fuzzy linear assignment method for multiattribute decision making with an application to spare parts inventory classification, Applied Soft Computing 42: 1–17. https://doi.org/10.1016/j.asoc.2016.01.031
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Bernardo, J. J.; Blin, J. M. 1977. A programming model of consumer choice among multi-attributed brands, Journal of Consumer Research 4(2): 111–118. https://doi.org/10.1086/208686
Chen, T. Y. 2013. A linear assignment method for multiple-criteria decision analysis with interval type-2 fuzzy sets, Applied Soft Computing 13(5): 2735–2748. https://doi.org/10.1016/j.asoc.2012.11.013
Chen, T. Y. 2014. The extended linear assignment method for multiple criteria decision analysis based on interval-valued intuitionistic fuzzy sets, Applied Mathematical Modeling 38(7–8): 2101–2117. https://doi.org/10.1016/j.apm.2013.10.017
Farhadnia, B. 2015. Multiple criteria decision-making methods with completely unknown weights in hesitant fuzzy linguistic term setting, Knowledge-Based Systems 93: 135–144. https://doi.org/10.1016/j.knosys.2015.11.008
Ginevičius, R. 2011. A new determining method for the criteria weights in multi-criteria evaluation, International Journal of Information Technology & Decision Making 10(6): 1067–1095. https://doi.org/10.1142/S0219622011004713
Grattan-Guinness, I. 1976. Fuzzy membership mapped onto interval and many-valued quantities, Mathematical Logic Quarterly 22(1): 149–160. https://doi.org/10.1002/malq.19760220120
Herrera, F.; Herrera-Viedma, E.; Verdegay, J. L. 1996. A model of consensus in group decision making under linguistic assessments, Fuzzy Sets Systems 78(1): 73–87. https://doi.org/10.1016/0165-0114(95)00107-7
Herrera, F.; Martinez, L. 2000. A 2-tuple fuzzy linguistic representation model for computing with words, IEEE Transactions on Fuzzy Systems 8(6): 746–752. https://doi.org/10.1109/91.890332
Hwang, C. L.; Yoon. K. P. 1995. Multiple attribute decision making: an introduction. Sage Publication Inc.: California. https://doi.org/10.1016/j.ins.2014.09.061
Lee, L. W.; Chen, S. M. 2015. Fuzzy decision making based on likelihood-based comparison relations of hesitant fuzzy linguistic term sets and hesitant fuzzy linguistic operators, Information Sciences 294: 513–529. https://doi.org/10.1016/j.ins.2014.09.061
Liang, Q.; Mendel, J. M. 2000. Interval type-2 fuzzy logic systems: theory and design, IEEE Transactions on Fuzzy Systems 8(5): 535–550. https://doi.org/10.1109/91.873577
Liao, H.; Xu, Z. 2015. Approaches to manage hesitant fuzzy linguistic information based on the cosine distance and similarity measures for HFLTSs and their application in qualitative decision making, Expert Systems with Applications 42: 5328–5336. https://doi.org/10.1016/j.eswa.2015.02.017
Liao, H.; Xu, Z.; Zeng, X. J. 2014. Distance and similarity measures for hesitant fuzzy linguistic term sets and their application in multi-criteria decision making, Information Sciences 271: 125–142. https://doi.org/10.1016/j.ins.2014.02.125
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Liao, H.; Xu, Z.; Zeng, X. J.; Merigó, J. M. 2015b. Qualitative decision making with correlation coefficients of hesitant fuzzy linguistic term sets, Knowledge-Based Systems 76: 127–138. https://doi.org/10.1016/j.knosys.2014.12.009
Lin, C. J.; Wen, U. P. 2004. A labeling algorithm for the fuzzy assignment problem, Fuzzy Sets and Systems 142(3): 20053–391. http://dx.doi.org/10.1016/S0165-0114(03)00017-4
Liu, H.; Rodríguez, R. M. 2014. A fuzzy envelope for hesitant fuzzy linguistic term set and its application to multi-criteria decision making, Information Sciences 258: 220–228. https://doi.org/10.1016/j.ins.2013.07.027
Liu, S. F.; Lin, Y. 2011. Grey systems theory and application. Heidelberg: Springer. https://doi.org/10.1007/978-3-642-16158-2
Martinez, L.; Herrera, F. 2010. An overview on the 2-tuple linguistic model for computing with words in decision making: extensions, applications and challenges, Information Science 207: 1–18. https://doi.org/10.1016/j.ins.2012.04.025
Montes, R.; Sánchez, A. M.; Villar, P.; Herrera, F. 2015. A web tool to support decision making in the housing market using hesitant fuzzy linguistic term sets, Applied Soft Computing 35: 949–957. https://doi.org/10.1016/j.asoc.2015.01.030
Razavi Hajiagha, S. H.; Amoozad Mahdiraji, H.; Hashemi, S. S. 2013. Multi-objective linear programming with interval coefficients: a fuzzy set based approach, Kybernetes 42(3): 482–496. https://doi.org/10.1108/03684921311323707
Razavi Hajiagha, S. H.; Amoozad Mahdiraji, H.; Hashemi, S. S. 2014a. A hybrid model of fuzzy goal programming and grey numbers in continuous project time, cost, and quality tradeoff, International Journal of Advanced Manufacturing Technology 71(1–4): 117–126. https://doi.org/10.1007/s00170-013-5463-2
Razavi Hajiagha, S. H.; Amoozad Mahdiraji, H.; Hashemi, S. S. 2015. Determining weights of fuzzy attributes for multi-attribute decision-making problems based on consensus of expert opinions, Technological and Economic Development of Economy 21(5): 738–755.
Razavi Hajiagha, S. H.; Amoozad Mahdiraji, H.; Hashemi, S. S.; Zavadskas, E. K. 2014b. Fuzzy multi objective programming based on comprise VIKOR method, International Journal of Information Technology and Decision Making 13(4): 679–699. https://doi.org/10.3846/20294913.2015.1058301
Razavi Hajiagha, S. H.; Amoozad Mahdiraji, H.; Zavadskas, E. K.; Hashemi, S. S. 2014c. Maximizing and minimizaing sets in solving fuzzy linear programming, Economic Computation and Economic Cybernetics Studies and Research 48(2): 113–133.
Rodríguez, R. M.; Martínez, L.; Herrera, F. 2012. Hesitant fuzzy linguistic terms sets for decision making, IEEE Transactions on Fuzzy Systems 20(1): 109–119. https://doi.org/10.1109/TFUZZ.2011.2170076
Rodríguez, R. M.; Martínez, L.; Herrera, F. 2013. A group decision making model dealing with comparative linguistic expressions based on hesitant fuzzy linguistic term set, Information Sciences 241: 28–42. https://doi.org/10.1016/j.ins.2013.04.006
Saaty, T. L. 1977. A scaling method for priorities in hierarchical structures, Journal of Mathematical Psychology 15(3): 234–281. https://doi.org/10.1016/0022-2496(77)90033-5
Saaty, T.; Ergu, D. 2015. When is a decision-making method trustworthy? criteria for evaluating multicriteria decision-making methods, International Journal of Information Technology and Decision Making 14(6): 1171–1188. https://doi.org/10.1142/S021962201550025X
Srinivasan, V.; Shocker, A. D. 1973. Linear programming techniques for multidimensional analysis of preferences, Psychometrika 38(3): 337–369. https://doi.org/10.1007/BF02291658
Torra, V. 2010. Hesitant fuzzy sets, International Journal of Intelligent Systems 25(6): 529–539. https://doi.org/10.1002/int.20418
Tzeng, G. H.; Huang, J. J. 2011. Multiple attribute decision making: methods and applications. Florida: CRC Press. https://doi.org/10.1201/b11032
Wang, H.; Xu, Z. 2015. Some consistency measures of extended hesitant fuzzy linguistic preference relations, Information Sciences 297: 316–331. https://doi.org/10.1016/j.ins.2014.10.047
Wang, J.; Wang, J. Q.; Zhang, H. Y. Chen, X. H. 2015. Multi-criteria decision-making based on hesitant fuzzy linguistic term sets: an outranking approach, Knowledge-Based Systems 86: 224–236. https://doi.org/10.1016/j.knosys.2015.06.007
Wei, C.; Ren, Z.; Rodríguez, R. M. 2015. A hesitant fuzzy linguistic TODIM method based on a score function, International Journal of Computational Intelligence Systems 8(4): 701–712. https://doi.org/10.1080/18756891.2015.1046329
Wei, C.; Zhao, N.; Tang, X. 2014. Operators and comparisons of hesitant fuzzy linguistic term sets, IEEE Transactions on Fuzzy Systems 22(3): 575–585. https://doi.org/10.1109/TFUZZ.2013.2269144
Wu, Z.; Xu, J. 2015. Managing consistency and consensus in group decision making with hesitant fuzzy linguistic preference relations, Omega 65: 28–4. https://doi.org/10.1016/j.omega.2015.12.005
Xia, M. M.; Xu, Z. S. 2011. Hesitant fuzzy information aggregation in decision making, International Journal of Approximate Reasoning 52(3): 395–407. https://doi.org/10.1016/j.ijar.2010.09.002
Xu, Z. S. 2004. Uncertain Multiple attribute decision making: methods and applications. Beijing: Tsinghua University Press. https://doi.org/10.1007/978-3-662-45640-8
Xu, Z. S. 2005. Deviation measures of linguistic preference relations in group decision making, Omega 33(3): 249–254. https://doi.org/10.1016/j.omega.2004.04.008
Xu, Z. S. 2012. Linguistic decision making: theory and methods. Beijing: Science Press. https://doi.org/10.1007/978-3-642-29440-2
Yu, P. L. 1990. Forming winning strategies: an integrated theory of habitual domains. Berlin: Springer. https://doi.org/10.1007/978-3-642-61295-4
Zadeh, L. A. 1965. Fuzzy sets, Information and Control 8(3): 338–353. https://doi.org/10.1016/S0019-9958(65)90241-X
Zadeh, L. A. 1975. The concept of a linguistic variable and its application to approximate reasoning – I, Information Sciences 8(3): 199–249. https://doi.org/10.1016/0020-0255(75)90036-5
Zamri, N.; Abdullah, L. 2015. A linear assignment method of simple additive weighting system in linear programming approach under interval type-2 fuzzy set concepts for MCDM problem, in H. Sulaiman, M. Othman, M. Othman, Y. Rahim, N. Pee (Eds.). Advanced computer and communication engineering technology. Lecture Notes in Electrical Engineering, vol 315. Springer, Cham, 833–842. https://doi.org/10.1007/978-3-319-07674-4_78
Zhang, Z.; Wu, C. 2014. On the use of multiplicative consistency in hesitant fuzzy linguistic preference relations, Knowledge-Based Systems 72: 13–27. https://doi.org/10.1016/j.knosys.2014.08.026
Zhu, B.; Xu, Z. 2014. Consistency measures for hesitant fuzzy linguistic preference relations, IEEE Transactions on Fuzzy Systems 22: 35–45. https://doi.org/10.1109/TFUZZ.2013.2245136
Zhu, B.; Xu, Z. 2016. Extended hesitant fuzzy sets, Technological and Economic Development of Economy 22(1): 100–121. https://doi.org/10.3846/20294913.2014.981882
Zimmerman, H. J. 1987. Fuzzy sets, decision making, and expert systems. Boston: Kluwer Academic Publisher. https://doi.org/10.1007/978-94-009-3249-4
Atanassov, K. 1986. Intuitionistic fuzzy sets, Fuzzy Sets and Systems 20(1): 87–96. http://dx.doi.org/10.1016/S0165-0114(86)80034-3
Atanassov, K.; Gargov, G. 1989. Interval valued intuitionistic fuzzy sets, Fuzzy Sets and Systems 31(3): 343–349. https://doi.org/10.1016/0165-0114(89)90205-4
Bashiri, M.; Badri, H.; Hejazi, T. H. 2011. Selecting optimum maintenance strategy by fuzzy interactive linear assignment method, Applied Mathematical Modeling 35(1): 152–164. https://doi.org/10.1016/j.apm.2010.05.014
Baykasoğlu, A.; Subulan, K.; Karaslan, F. S. 2016. A new fuzzy linear assignment method for multiattribute decision making with an application to spare parts inventory classification, Applied Soft Computing 42: 1–17. https://doi.org/10.1016/j.asoc.2016.01.031
Bellman, R. E.; Zadeh, L. A. 1970. Decision-making in a fuzzy environment, Management Science 17(4): 141–164. https://doi.org/10.1287/mnsc.17.4.B141
Bernardo, J. J.; Blin, J. M. 1977. A programming model of consumer choice among multi-attributed brands, Journal of Consumer Research 4(2): 111–118. https://doi.org/10.1086/208686
Chen, T. Y. 2013. A linear assignment method for multiple-criteria decision analysis with interval type-2 fuzzy sets, Applied Soft Computing 13(5): 2735–2748. https://doi.org/10.1016/j.asoc.2012.11.013
Chen, T. Y. 2014. The extended linear assignment method for multiple criteria decision analysis based on interval-valued intuitionistic fuzzy sets, Applied Mathematical Modeling 38(7–8): 2101–2117. https://doi.org/10.1016/j.apm.2013.10.017
Farhadnia, B. 2015. Multiple criteria decision-making methods with completely unknown weights in hesitant fuzzy linguistic term setting, Knowledge-Based Systems 93: 135–144. https://doi.org/10.1016/j.knosys.2015.11.008
Ginevičius, R. 2011. A new determining method for the criteria weights in multi-criteria evaluation, International Journal of Information Technology & Decision Making 10(6): 1067–1095. https://doi.org/10.1142/S0219622011004713
Grattan-Guinness, I. 1976. Fuzzy membership mapped onto interval and many-valued quantities, Mathematical Logic Quarterly 22(1): 149–160. https://doi.org/10.1002/malq.19760220120
Herrera, F.; Herrera-Viedma, E.; Verdegay, J. L. 1996. A model of consensus in group decision making under linguistic assessments, Fuzzy Sets Systems 78(1): 73–87. https://doi.org/10.1016/0165-0114(95)00107-7
Herrera, F.; Martinez, L. 2000. A 2-tuple fuzzy linguistic representation model for computing with words, IEEE Transactions on Fuzzy Systems 8(6): 746–752. https://doi.org/10.1109/91.890332
Hwang, C. L.; Yoon. K. P. 1995. Multiple attribute decision making: an introduction. Sage Publication Inc.: California. https://doi.org/10.1016/j.ins.2014.09.061
Lee, L. W.; Chen, S. M. 2015. Fuzzy decision making based on likelihood-based comparison relations of hesitant fuzzy linguistic term sets and hesitant fuzzy linguistic operators, Information Sciences 294: 513–529. https://doi.org/10.1016/j.ins.2014.09.061
Liang, Q.; Mendel, J. M. 2000. Interval type-2 fuzzy logic systems: theory and design, IEEE Transactions on Fuzzy Systems 8(5): 535–550. https://doi.org/10.1109/91.873577
Liao, H.; Xu, Z. 2015. Approaches to manage hesitant fuzzy linguistic information based on the cosine distance and similarity measures for HFLTSs and their application in qualitative decision making, Expert Systems with Applications 42: 5328–5336. https://doi.org/10.1016/j.eswa.2015.02.017
Liao, H.; Xu, Z.; Zeng, X. J. 2014. Distance and similarity measures for hesitant fuzzy linguistic term sets and their application in multi-criteria decision making, Information Sciences 271: 125–142. https://doi.org/10.1016/j.ins.2014.02.125
Liao, H.; Xu, Z.; Zeng, X. J. 2015a. Hesitant fuzzy linguistic VIKOR method and its application in qualitative multiple criteria decision making, IEEE Transactions on Fuzzy Systems 23: 1343–1355. https://doi.org/10.1109/TFUZZ.2014.2360556
Liao, H.; Xu, Z.; Zeng, X. J.; Merigó, J. M. 2015b. Qualitative decision making with correlation coefficients of hesitant fuzzy linguistic term sets, Knowledge-Based Systems 76: 127–138. https://doi.org/10.1016/j.knosys.2014.12.009
Lin, C. J.; Wen, U. P. 2004. A labeling algorithm for the fuzzy assignment problem, Fuzzy Sets and Systems 142(3): 20053–391. http://dx.doi.org/10.1016/S0165-0114(03)00017-4
Liu, H.; Rodríguez, R. M. 2014. A fuzzy envelope for hesitant fuzzy linguistic term set and its application to multi-criteria decision making, Information Sciences 258: 220–228. https://doi.org/10.1016/j.ins.2013.07.027
Liu, S. F.; Lin, Y. 2011. Grey systems theory and application. Heidelberg: Springer. https://doi.org/10.1007/978-3-642-16158-2
Martinez, L.; Herrera, F. 2010. An overview on the 2-tuple linguistic model for computing with words in decision making: extensions, applications and challenges, Information Science 207: 1–18. https://doi.org/10.1016/j.ins.2012.04.025
Montes, R.; Sánchez, A. M.; Villar, P.; Herrera, F. 2015. A web tool to support decision making in the housing market using hesitant fuzzy linguistic term sets, Applied Soft Computing 35: 949–957. https://doi.org/10.1016/j.asoc.2015.01.030
Razavi Hajiagha, S. H.; Amoozad Mahdiraji, H.; Hashemi, S. S. 2013. Multi-objective linear programming with interval coefficients: a fuzzy set based approach, Kybernetes 42(3): 482–496. https://doi.org/10.1108/03684921311323707
Razavi Hajiagha, S. H.; Amoozad Mahdiraji, H.; Hashemi, S. S. 2014a. A hybrid model of fuzzy goal programming and grey numbers in continuous project time, cost, and quality tradeoff, International Journal of Advanced Manufacturing Technology 71(1–4): 117–126. https://doi.org/10.1007/s00170-013-5463-2
Razavi Hajiagha, S. H.; Amoozad Mahdiraji, H.; Hashemi, S. S. 2015. Determining weights of fuzzy attributes for multi-attribute decision-making problems based on consensus of expert opinions, Technological and Economic Development of Economy 21(5): 738–755.
Razavi Hajiagha, S. H.; Amoozad Mahdiraji, H.; Hashemi, S. S.; Zavadskas, E. K. 2014b. Fuzzy multi objective programming based on comprise VIKOR method, International Journal of Information Technology and Decision Making 13(4): 679–699. https://doi.org/10.3846/20294913.2015.1058301
Razavi Hajiagha, S. H.; Amoozad Mahdiraji, H.; Zavadskas, E. K.; Hashemi, S. S. 2014c. Maximizing and minimizaing sets in solving fuzzy linear programming, Economic Computation and Economic Cybernetics Studies and Research 48(2): 113–133.
Rodríguez, R. M.; Martínez, L.; Herrera, F. 2012. Hesitant fuzzy linguistic terms sets for decision making, IEEE Transactions on Fuzzy Systems 20(1): 109–119. https://doi.org/10.1109/TFUZZ.2011.2170076
Rodríguez, R. M.; Martínez, L.; Herrera, F. 2013. A group decision making model dealing with comparative linguistic expressions based on hesitant fuzzy linguistic term set, Information Sciences 241: 28–42. https://doi.org/10.1016/j.ins.2013.04.006
Saaty, T. L. 1977. A scaling method for priorities in hierarchical structures, Journal of Mathematical Psychology 15(3): 234–281. https://doi.org/10.1016/0022-2496(77)90033-5
Saaty, T.; Ergu, D. 2015. When is a decision-making method trustworthy? criteria for evaluating multicriteria decision-making methods, International Journal of Information Technology and Decision Making 14(6): 1171–1188. https://doi.org/10.1142/S021962201550025X
Srinivasan, V.; Shocker, A. D. 1973. Linear programming techniques for multidimensional analysis of preferences, Psychometrika 38(3): 337–369. https://doi.org/10.1007/BF02291658
Torra, V. 2010. Hesitant fuzzy sets, International Journal of Intelligent Systems 25(6): 529–539. https://doi.org/10.1002/int.20418
Tzeng, G. H.; Huang, J. J. 2011. Multiple attribute decision making: methods and applications. Florida: CRC Press. https://doi.org/10.1201/b11032
Wang, H.; Xu, Z. 2015. Some consistency measures of extended hesitant fuzzy linguistic preference relations, Information Sciences 297: 316–331. https://doi.org/10.1016/j.ins.2014.10.047
Wang, J.; Wang, J. Q.; Zhang, H. Y. Chen, X. H. 2015. Multi-criteria decision-making based on hesitant fuzzy linguistic term sets: an outranking approach, Knowledge-Based Systems 86: 224–236. https://doi.org/10.1016/j.knosys.2015.06.007
Wei, C.; Ren, Z.; Rodríguez, R. M. 2015. A hesitant fuzzy linguistic TODIM method based on a score function, International Journal of Computational Intelligence Systems 8(4): 701–712. https://doi.org/10.1080/18756891.2015.1046329
Wei, C.; Zhao, N.; Tang, X. 2014. Operators and comparisons of hesitant fuzzy linguistic term sets, IEEE Transactions on Fuzzy Systems 22(3): 575–585. https://doi.org/10.1109/TFUZZ.2013.2269144
Wu, Z.; Xu, J. 2015. Managing consistency and consensus in group decision making with hesitant fuzzy linguistic preference relations, Omega 65: 28–4. https://doi.org/10.1016/j.omega.2015.12.005
Xia, M. M.; Xu, Z. S. 2011. Hesitant fuzzy information aggregation in decision making, International Journal of Approximate Reasoning 52(3): 395–407. https://doi.org/10.1016/j.ijar.2010.09.002
Xu, Z. S. 2004. Uncertain Multiple attribute decision making: methods and applications. Beijing: Tsinghua University Press. https://doi.org/10.1007/978-3-662-45640-8
Xu, Z. S. 2005. Deviation measures of linguistic preference relations in group decision making, Omega 33(3): 249–254. https://doi.org/10.1016/j.omega.2004.04.008
Xu, Z. S. 2012. Linguistic decision making: theory and methods. Beijing: Science Press. https://doi.org/10.1007/978-3-642-29440-2
Yu, P. L. 1990. Forming winning strategies: an integrated theory of habitual domains. Berlin: Springer. https://doi.org/10.1007/978-3-642-61295-4
Zadeh, L. A. 1965. Fuzzy sets, Information and Control 8(3): 338–353. https://doi.org/10.1016/S0019-9958(65)90241-X
Zadeh, L. A. 1975. The concept of a linguistic variable and its application to approximate reasoning – I, Information Sciences 8(3): 199–249. https://doi.org/10.1016/0020-0255(75)90036-5
Zamri, N.; Abdullah, L. 2015. A linear assignment method of simple additive weighting system in linear programming approach under interval type-2 fuzzy set concepts for MCDM problem, in H. Sulaiman, M. Othman, M. Othman, Y. Rahim, N. Pee (Eds.). Advanced computer and communication engineering technology. Lecture Notes in Electrical Engineering, vol 315. Springer, Cham, 833–842. https://doi.org/10.1007/978-3-319-07674-4_78
Zhang, Z.; Wu, C. 2014. On the use of multiplicative consistency in hesitant fuzzy linguistic preference relations, Knowledge-Based Systems 72: 13–27. https://doi.org/10.1016/j.knosys.2014.08.026
Zhu, B.; Xu, Z. 2014. Consistency measures for hesitant fuzzy linguistic preference relations, IEEE Transactions on Fuzzy Systems 22: 35–45. https://doi.org/10.1109/TFUZZ.2013.2245136
Zhu, B.; Xu, Z. 2016. Extended hesitant fuzzy sets, Technological and Economic Development of Economy 22(1): 100–121. https://doi.org/10.3846/20294913.2014.981882
Zimmerman, H. J. 1987. Fuzzy sets, decision making, and expert systems. Boston: Kluwer Academic Publisher. https://doi.org/10.1007/978-94-009-3249-4