Optimal Solution of Nonlinear Fuzzy Optimization Problem under Linear Order Relation

Multi-variable nonlinear fuzzy optimization problem is considered under linear order relation on fuzzy numbers. Using gH-differentiability of a fuzzy-valued function $\tilde{f}$, new necessary and sufficient optimality conditions are proposed. The optimality conditions are obtained without putting additional conditions on fuzzy-valued functions like, convexity, quasi-convexity, pseudo-convexity. Optimum solution of the fuzzy optimization problem is obtained based on the optimality conditions. Illustrations and a case study are given to explain the numerical applications of the proposed results. Comparison of optimality conditions from existing literature is given.