Differentiability and optimality of a fuzzy function

TL;DR

This paper introduces a differentiability concept for fuzzy functions and establishes a necessary and sufficient condition for optimality in fuzzy optimization problems.

Contribution

It proposes a new differentiability notion for fuzzy functions and provides a criterion for optimality in fuzzy optimization.

Findings

Defined a new differentiability concept for fuzzy functions

Proved a necessary and sufficient condition for optimality

Applied the concept to obtain non-dominated solutions

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.