Abstract
Fuzzy extension of a Multi-Criteria Decision Analysis (MCDA) method implies a choice of an approach to assessing corresponding functions of fuzzy variables along with a method for ordering alternatives based on ranking of fuzzy quantities. The primary objective of this contribution is the development and comparison of Fuzzy MCDA (FMCDA) models, which represent different approaches to fuzzy extension of an ordinary MCDA method. For this, three approaches to assessing functions of fuzzy numbers are considered (approximate method, standard fuzzy arithmetic, and transformation method), as well as four methods for ranking of fuzzy numbers (two defuzzification methods - centroid index and integral of means, as well as modifications of these methods, which are pairwise comparison ranking methods intended to rank dependent fuzzy numbers). In this paper, distinctions in ranking alternatives by different FMCDA models, which are fuzzy extensions of an ordinary MCDA method TOPSIS as an example, are explored with the use of Monte Carlo simulation. In addition, the significance of distinctions is explored based on a granulation of the output information. According to the studies, distinctions in ranking alternatives by different FMCDA models may be considered as significant both for ranking and choice MCDA problems. This research is original and has no analogues.
Supported by the Russian National research project RFBR-19-07-01039.
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References
Chen, C.T.: Extensions of the TOPSIS for group decision-making under fuzzy environment. Fuzzy Sets Syst. 114(1), 1–9 (2000)
Chen, S., Hwang, C.: Fuzzy Multiple Attribute Decision Making: Methods and Applications, vol. 375. Springer, Berlin (1992). https://doi.org/10.1007/978-3-642-46768-4
Hanss, M.: Applied Fuzzy Arithmetic. Springer, Heidelberg (2005). https://doi.org/10.1007/b138914
Kahraman, C., Onar, S.C., Oztaysi, B.: Fuzzy multicriteria decision-making: a literature review. Int. J. Comput. Intell. Syst. 8(4), 637–666 (2015)
Kahraman, C., Tolga, A.: An alternative ranking approach and its usage in multi-criteria decision-making. Int. J. Comput. Intell. Syst. 2(3), 219–235 (2009)
Kaya, T., Kahraman, C.: Multicriteria decision making in energy planning using a modified fuzzy TOPSIS methodology. Expert Syst. Appl. 38(6), 6577–6585 (2011)
Klir, G., Yuan, B.: Fuzzy Sets and Fuzzy Logic: Theory and Applications. Simon & Schuster, Upper Saddle River (1995)
Lima Junior, F., Osiro, L., Ribeiro Carpinetti, L.: A comparison between Fuzzy AHP and Fuzzy TOPSIS methods to supplier selection. Appl. Soft Comput. 21, 194–209 (2014). https://doi.org/10.1016/j.asoc.2014.03.014
Nguyen, H., Kreinovich, V., Wu, B., Xiang, G.: Computing Statistics under Interval and Fuzzy Uncertainty. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-24905-1
Ploskas, N., J., P.: A decision support system for multiple criteria alternative ranking using TOPSIS and VIKOR in fuzzy and nonfuzzy environments. Fuzzy Sets Syst. 377 (2019) .https://doi.org/10.1016/j.fss.2019.01.012
Wang, X., Kerre, E.: Reasonable properties for the ordering of fuzzy quantities (I). Fuzzy Sets Syst. 118(3), 375–385 (2001)
Wang, X., Kerre, E.: Reasonable properties for the ordering of fuzzy quantities (II). Fuzzy Sets Syst. 118(3), 387–405 (2001)
Wang, X., Ruan, D., Kerre, E.: Mathematics of Fuzziness Basic Issues. Springer, Heidelberg (2009). https://doi.org/10.1007/978-3-540-78311-4
Yager, R.: On choosing between fuzzy subsets. Kybernetes 9(2), 151–154 (1980)
Yager, R.: A procedure for ordering fuzzy subsets of the unit interval. Inf. Sci. 24(2), 143–161 (1981)
Yatsalo, B., Korobov, Radaev, A., Qin, J., Martínez, L.: Ranking of independent and dependent fuzzy numbers and intransitivity in fuzzy MCDA. IEEE Trans. Fuzzy Syst PP(99), 1 (2021). https://doi.org/10.1109/TFUZZ.2021.3058613
Yatsalo, B., Korobov, A.: Different approaches to fuzzy extension of an MCDA method and their comparison. In: Kahraman, C., Cevik Onar, S., Oztaysi, B., Sari, I., Cebi, S., Tolga, A. (eds.) Intelligent and Fuzzy Techniques: Smart and Innovative Solutions. INFUS 2020. Advances in Intelligent Systems and Computing, vol. 1197, pp. 709–717. Springer, Cham (2021). https://doi.org/10.1007/978-3-030-51156-2_82
Yatsalo, B., Korobov, A., Martínez, L.: From MCDA to fuzzy MCDA: violation of basic axioms and how to fix it. Neural Comput. Appl. 33(3) (2021). https://doi.org/10.1007/s00521-020-05053-9
Yatsalo, B., Korobov, A., Oztaysi, B., Kahraman, C., Martínez, L.: A general approach to Fuzzy TOPSIS based on the concept of fuzzy multicriteria acceptability analysis. J. Intell. Fuzzy Syst. 38, 979–995 (2020)
Yuan, Y.: Criteria for evaluating fuzzy ranking methods. Fuzzy Sets Syst. 44, 139–157 (1991)
Zadeh, L.: The concept of a linguistic variable and its applications to approximate reasoning. Inf. Sci., Part I, II, III (8,9), 199–249, 301–357, 43–80 (1975)
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Korobov, A., Radaev, A., Yatsalo, B. (2022). How Different Are Fuzzy MCDA Models, Which are Fuzzy Extensions of an MCDA Method?. In: Kahraman, C., Cebi, S., Cevik Onar, S., Oztaysi, B., Tolga, A.C., Sari, I.U. (eds) Intelligent and Fuzzy Techniques for Emerging Conditions and Digital Transformation. INFUS 2021. Lecture Notes in Networks and Systems, vol 307. Springer, Cham. https://doi.org/10.1007/978-3-030-85626-7_45
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