Maximizing alternatives to the decision-making problem with a goal type-2 fuzzy set / Mashchenko. (2019)
Ukrainian

English  Cybernetics and Systems Analysis   /     Issue (2019, 55 (6))

Mashchenko S.O.
Maximizing alternatives to the decision-making problem with a goal type-2 fuzzy set

The Bellman and Zadeh approach is applied to a decision-making problem posed on type-2 fuzzy sets (T2FSs). The concept of a solution T2FS is defined. The natural order relation was extende to the class of fuzzy sets to compare fuzzy sets of membership degrees of alternatives. Based on this preference relation, a fuzzy set of nondominated alternatives is constructed. The concept of a nondominated alternative of level α is introduced. It is shown that such an alternative can be obtained from the optimization problem in which the primary membership degree of a T2FS of solutions is maximized under a constrained secondary degree. The existence of nondominated alternatives of level α = 1 is investigated. The problem of choosing alternatives by two criteria (the primary and secondary degrees of membership in the T2FS of solutions) is formulated. © 2019, Springer Science+Business Media, LLC, part of Springer Nature.

Keywords: decision-making, fuzzy mathematical programming, fuzzy set, type-2 fuzzy set, Constrained optimization, Fuzzy sets, Mathematical programming, Decision-making problem, Fuzzy mathematical programming, Membership degrees, Optimization problems, Order relation, Preference relation, Type-2 fuzzy set, Decision making


Cite:
Mashchenko S.O. (2019). Maximizing alternatives to the decision-making problem with a goal type-2 fuzzy set. Cybernetics and Systems Analysis, 55 (6), 62–72. doi: https://doi.org/10.1007/s10559-019-00203-x http://jnas.nbuv.gov.ua/article/UJRN-0001044332 [In Russian].


 

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