Non-dominated Solution of Fuzzy Maximum-Return Problem

TL;DR

This paper introduces a method to find non-dominated solutions for fuzzy maximum-return problems using Newton's method, leveraging the differentiability of fuzzy functions and fuzzy number ordering.

Contribution

It develops a Newton-based approach for solving unconstrained single-variable fuzzy optimization problems, which is a novel application in fuzzy optimization.

Findings

Successfully applied Newton's method to fuzzy maximum-return problems.

Established differentiability conditions for fuzzy-valued functions.

Provided a framework for non-dominated solution identification in fuzzy optimization.

Abstract

In this paper, we find a non-dominated solution of a fuzzy maximum-return problem ( unconstrained single-variable fuzzy optimization problem ) . We establish Newton method to find the solution of the unconstrained single-variable fuzzy optimization problem using the differentiability of $\alpha$-level functions of a fuzzy-valued function and partial order relation on a set of fuzzy numbers.