Maximizing Alternatives in a 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.