UDC 519.8
MAXIMIZING ALTERNATIVES TO THE DECISION-MAKING PROBLEM WITH A GOAL
TYPE-2 FUZZY SET
Abstract. The Bellman and Zadeh approach is applied to the decision-making problem, which is defined on type-2 fuzzy sets (T2FSs).
T2FS Solution is defined. An extension of the natural order ratio to the class of fuzzy sets is used for comparison of fuzzy sets of alternatives membership degrees.
A fuzzy set of non-dominated alternatives is constructed by this preference relation.
The notion of the α-level non-dominated alternative is introduced. It is shown that this is an optimization problem solution.
In this problem, the primary membership degree of a T2FS solution is maximized with a constrained secondary degree.
The existence of 1-level non-dominated alternatives is investigated.
The problem of choosing alternatives by two criteria (the primary and secondary degrees of membership to the T2FS solution) is formulated.
Keywords: a fuzzy set, a type-2 fuzzy set, fuzzy mathematical programming, decision making.
FULL TEXT
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