Fuzzy optimization in gH- symmetrically differentiable fuzzy function of several variables

Abstract

This paper defines a new concept called Levelwise generalized hukuhara symmetric ( $\mathrm{LgHs})$ derivative of functions which are of fuzzy valued and with several variables. We can see that $\mathrm{LgH}$ derivative of functions which are of fuzzy valued and with several variables is very much general compared to existing ones. Here we introduced a concept of midpoint and radius function. This allows us for a connection between generalized hukuhara symmetric ( $\mathrm{gHs}$ ) differentiability and classic definitions for the cases of differentiability in functions which are real valued. The novel directional $\mathrm{LgH}$ derivative and partial $\mathrm{gHs}$ derivative unifies and extends in latest papers.