Abstract
Pythagorean fuzzy sets (PFS) is proposed by Yager, which characterized by a membership, nonmembership and hesitation degree. The condition that the square sum of its membership and nonmembership degree is less than or equal to one and is very useful for decision makers (DMs) to depict the fuzzy character of data comprehensively. It is hypothesized that the PFS is also capable to model uncertainty and impreciseness in the practical decision making problems. A handful of research focused on Vlsekriterijumska Optimizacija I Kompromisno Resenje (VIKOR) method based on IFS but no one pay attention to propose the new VIKOR based on PFS. Therefore, the purpose of this paper is to propose the PFS for VIKOR method. This study uses Pythagorean fuzzy sets to handle the linguistic uncertainty and imprecision of human beings judgment. Finally, the compromise solution can be obtained. An illustrative example is demonstrated to show their practicality and effectiveness of the proposed VIKOR based on PFS.
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References
Hwang, C.L., Yoon, K.S.: Multiple Attribute Decision Methods and Applications. Springer, Berlin, Germany (1981)
Roy, B., Bertier, P.: La méthode ELECTRE II: une méthode de classement en prédence de critères multiples (1971)
Mareschal, B., Brans, J.P., Vincke, P.: PROMETHEE: A New Family of Outranking Methods in Multicriteria Analysis. Universite Libre de Bruxelles, ULB (1984)
Opricovic, S.: Multicriteria optimization of civil engineering systems. Fac. Civ. Eng., Belgrade (1998)
Zadeh, L.A.: Fuzzy sets. Inf. Control 8, 338–353 (1965)
Bellman, R.E., Zadeh, L.A.: Decision-making in a fuzzy environment. Manag. Sci. 17, 141–161 (1970)
Yager, R.R.: Fuzzy decision making including unequal objectives. Fuzzy Sets Syst. 1, 87–95 (1978)
Nakamura, K.: Preference relations on a set of fuzzy utilities as a basis for decision making. Fuzzy Sets Syst. 20, 147–162 (1986)
Atanassov, K.T.: Intuitionistic fuzzy sets. Fuzzy Sets Syst. 20, 87–96 (1986)
Xu, Z.S., Yager, R.R.: Dynamic intuitionistic fuzzy multi-attribute decision making. Int. J. Approx. Reason. 48, 246–262 (2008)
Liu, H.W., Wang, G.J.: Multi-criteria decision-making methods based on intuitionistic fuzzy sets. Eur. J. Oper. Res. 179, 220–233 (2007)
Boran, F.E., Genc, S., Kurt, M.: A multi-criteria intuitionistic fuzzy group decision making for supplier selection with TOPSIS method. Exp. Syst. Appl. 36, 11363–11368 (2009)
Yager, R.R.: Pythagorean fuzzy subsets. In: Proceeding of the Joint IFSA World Congress and NAFIPS Annual Meeting, Edmonton, Canada, pp. 57–61 (2013)
Zeng, S., Chen, J., Li, X.: A hybrid method for Pythagorean fuzzy multiple-criteria decision making. Int. J. Inf. Technol. Decis. Mak. 14, 1–16 (2015). https://doi.org/10.1142/S0219622016500012
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Mohd, W.R.W., Abdullah, L. (2019). The VIKOR Method with Pythagorean Fuzzy Sets and Their Applications. In: Kor, LK., Ahmad, AR., Idrus, Z., Mansor, K. (eds) Proceedings of the Third International Conference on Computing, Mathematics and Statistics (iCMS2017). Springer, Singapore. https://doi.org/10.1007/978-981-13-7279-7_24
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DOI: https://doi.org/10.1007/978-981-13-7279-7_24
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