Best approximation results for fuzzy-number-valued continuous functions

TL;DR

This paper investigates optimal approximation of fuzzy-number-valued continuous functions by real-valued functions, introducing a new distance measure and proving existence results using the Michael Selection Theorem.

Contribution

It introduces a novel method to measure distances between fuzzy and real-valued functions and establishes the existence of best approximations in this context.

Findings

Existence of best approximation proven using Michael Selection Theorem

New distance measure between fuzzy and real-valued functions introduced

Framework for approximating fuzzy functions with real-valued functions developed

Abstract

In this paper we study the best approximation of a fixed fuzzy-number-valued continuous function to a subset of fuzzy-number-valued continuous functions. We also introduce a method to measure the distance between a fuzzy-number-valued continuous function and a real-valued one. Then we prove the existence of the best approximation of a fuzzy-number-valued continuous function to the space of real-valued continuous functions by using the well-known Michael Selection Theorem.