Fuzzy convexity with application to fuzzy decision making

Abstract

Based on the more restrictive definition of fuzzy convexity due to Ammar and Metz, some useful extremum properties are developed. We prove that any local maximizer of a convex fuzzy set is also a global maximizer, and that any strictly local maximizer of a quasiconvex fuzzy set is also a global maximizer. We also study the class of strictly convex (resp. strictly quasiconvex) fuzzy sets that is more restrictive than the class of convex (resp. quasiconvex) fuzzy sets. We prove that for both families of strictly convex and strictly quasiconvex fuzzy sets, every local maximizer is also the unique global maximizer. Finally, some composition rules for convex fuzzy sets are given and some applications to fuzzy decision making are discussed.