E-concavity for Fuzzy Sets

Almost all practically encountered decision making problems can be treated as fuzzy decision making problems. In Bellman and Zadeh´s seminal approach, fuzzy decision making problems are essentially reduced to the maximization of the aggregated objectives and constraints. Thus, the study of the properties of concavity before and after aggregation should be the a very useful approach for solving fuzzy decision making problems. In this paper, the concept of E-convex, which covers a wider class of sets and functions, is extended to fuzzy sets. Supp-E-concave and supp-E-quasiconcave fuzzy sets are first introduced. Then some aggregation rules for supp-E-concave and supp-E-quasiconcave fuzzy sets are given. Finally, some useful composition rules are developed. These aggregation and composition rules should form the basis for further exploration of fuzzy E convex sets in fuzzy decision-making