Duality theorems in fuzzy mathematical programming problems based on the concept of necessity

Abstract

The fuzzy-valued Lagrangian function for the fuzzy mathematical programming problem via the concept of the fuzzy scalar (inner) product is proposed. A solution concept of fuzzy optimization problems, which is essentially similar to the notion of Pareto solution in multiobjective programming problems, is also introduced by ranking the fuzzy numbers using the necessity indices. Under these settings, the weak and strong duality theorems can be elicited. We show that the primal and dual fuzzy mathematical programming problems have no duality gap under suitable convexity assumptions for fuzzy-valued functions.