The KKT Optimality Conditions and Duality for Constrained Programming Problem with Generalized α- Convex Fuzzy Functions

Abstract

This paper mainly studies the mixed constraint interval programming problem under the generalized convex fuzzy mapping. Firstly, this paper give the concepts of fuzzy mappings, such as quasiconvex, strictly quasiconvex, pseudoconvex and strictly pseudoconvex. Then, the relation of generalized convex fuzzy mapping is studied and some properties are obtained. Finally, the necessary and sufficient KKT conditions are given, and the duality problem is established. The weak duality, strong duality and inverse duality theorem of fuzzy interval programming are proved.