Mashchenko S.O.
Non-dominated alternatives of fuzzy set of expert

The author analyzes a set of non-dominated alternatives in the problem of group decision-making by a fuzzy set of experts and shows that it is a type-2 fuzzy set (T2FS). The corresponding type-2 membership function is generated. The decomposition approach is used to analyze the T2FS of non-dominated alternatives. It is shown that the T2FS of non-dominated alternatives can be decomposed according to secondary membership degrees into a finite set of type-1 fuzzy sets, each being a set of non-dominated alternatives for a crisp set of experts, which is the corresponding α-cut of the original fuzzy set. Examples are given. © 2023, Springer Science+Business Media, LLC, part of Springer Nature.

Keywords: decision-making, fuzzy preference relation, type-2 fuzzy set, Fuzzy sets, Membership functions, Decisions makings, Decomposition approach, Finite set, Fuzzy preference relations, Group Decision Making, Membership degrees, Memberships function, Secondary memberships, Type-1 fuzzy sets, Type-2 fuzzy set, Decision making

Cite:
Mashchenko S.O. (2023). Non-dominated alternatives of fuzzy set of expert. Cybernetics and Systems Analysis, 59 (3), 59–70. doi: https://doi.org/10.1007/s10559-023-00575-1 http://jnas.nbuv.gov.ua/article/UJRN-0001402509 [In Ukrainian].