Harmonic Convex and Concave Fuzzy Mappings with Differentiability

Abstract

This research we specifically examined harmonic convex (H-convex) and harmonic concave (H-concave) fuzzy mappings using the principle of differentiability coined by Goetschel and Voxman, and some interrelationships were obtained between differentiable H-convex fuzzy mappings and generalized convex fuzzy mappings like pseudoconvex (pseudoconcave) and quasiconvex (quasiconcave) fuzzy mappings. In addition, differentiable H-convex fuzzy mappings were used to research the KKT conditions for the Harmonic convex fuzzy programming problem (HCFP), the effects of duality, and minmax. Additionally, the findings were explained with sufficient instances.

Keywords:Duality results; Fuzzy optimization; H-convex and H-concave fuzzy mappings; KKT conditions; Minmaxproblem