Relations of endograph metric and $\Gamma$-convergence on fuzzy sets

TL;DR

This paper demonstrates the compatibility between the endograph metric and $\Gamma$-convergence on a broad class of fuzzy sets in Euclidean space, enhancing understanding of convergence behaviors in fuzzy set theory.

Contribution

It establishes the relationship between the endograph metric and $\Gamma$-convergence for fuzzy sets, providing a unified framework for analyzing fuzzy set convergence.

Findings

Endograph metric and $\Gamma$-convergence are compatible on many fuzzy sets.

The results facilitate better analysis of fuzzy set convergence.

The work broadens the theoretical understanding of fuzzy set metrics.

Abstract

This paper shows that the endograph metric and the $\Gamma$-convergence are compatible on a large class of fuzzy set in $\mathbb{R}^m$.