Saddle Point Optimality Conditions in Fuzzy Optimization Problems

The Karush–Kuhn–Tucker (KKT) optimality conditions and saddle point optimality conditions in fuzzy programming problems have been studied in literature by various authors under different conditions. In this paper, by considering a partial order relation on the set of fuzzy numbers, and convexity with differentiability of fuzzy mappings, we have obtained the Fritz John (FJ) constraint qualification and KKT necessary conditions for a fuzzy optimization problem with fuzzy coefficients, for first time. Owing to the help of the KKT optimality conditions, we then discuss, the saddle point optimality conditions, associated with a fuzzy optimization problem under convexity and differentiability of fuzzy mappings.

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