KKT optimality conditions for fuzzy optimization problems using \({H}^{1}\) and \({H}^{2}\) derivative

This paper purposes a new concept of differentiability to obtain optimality conditions for Fuzzy Optimization Problems with fuzzy number valued objective function in a Quasi-linear metric space. Hukuhara differentiability (H-differentiability) and generalized Hukuhara differentiability (gH-differentiability) are the widely adapted concepts of differentiability in literature. A core issue open to exploration is how to optimize a fuzzy objective function which is neither gH-differentiable nor H-differentiable. We derive modified Karush–Kuhn–Tucker (KKT) conditions using the concept of \({H}^{1}\) $H^1$ and \({H}^{2}\) $H^2$ differentiability, which is a generalization of the widely used Hukuhara differentiability (H-differentiability) and generalized Hukuhara differentiability (gH-differentiability). Numerical illustrations have been provided to validate the obtained results. The conditions derived in this paper cover a significantly wider range of functions as compared to the previous works which uses H-differentiability and gH-differentiability.