Differentiability and optimality of a fuzzy function

Abstract

In this article, we introduce a differentiability concept for fuzzy functions $\tilde{f}:F(\mathbb{R})\to F(\mathbb{R})$, where $F(\mathbb{R})$ is the set of all fuzzy numbers. With the help of the proposed differentiability notion, we prove a necessary and sufficient condition for optimality to obtain a non-dominated solution of a fuzzy optimization problem.

Submitted to Journal