Subdifferential of fuzzy n-cell number valued functions and its applications in optimization problems

TL;DR

This paper introduces a new subdifferential concept for fuzzy n-cell number valued functions, establishes related theorems, and applies these to optimization problems such as Lagrangian duality and composite minimization.

Contribution

It proposes a novel subdifferential definition for fuzzy n-cell number valued functions and explores its theoretical properties and applications in optimization.

Findings

Established subdifferentiability theorems for the new concept

Applied the subdifferential to Lagrangian dual problems

Addressed minimization of composite fuzzy functions

Abstract

In this paper, we present the concept of subdifferential for fuzzy n-cell number valued functions. Then we state some theorems related to subdifferentiability based on the new definition. Finally, we present some applications emphasized on optimization problems, including the Lagrangian dual problem and minimizing the composite problem.