A groupoid approach to the study of fuzzy topological spaces

TL;DR

This paper introduces a novel algebraic approach using groupoids to better understand the complement operation in fuzzy topological spaces, bridging the gap between fuzzy and classical topology.

Contribution

It proposes associating fuzzy topological spaces with classical topological spaces via groupoids and the Lasso topology to characterize fuzzy complement operations.

Findings

Established a topological characterization of fuzzy complement using groupoids.

Connected fuzzy topology concepts with classical topological structures.

Provided a new algebraic framework for fuzzy topological space analysis.

Abstract

The definition of the complement of a fuzzy subset is algebraic in nature and when it is used in the context of fuzzy topological spaces it does not share any similarity with the usual property of topological spaces that the complement of an open subset is closed. To tackle this inconsistency, we associate to any fuzzy topological space a topological space and use its fundamental groupoid equipped with the Lasso topology to give a topological characterization for the complementation of fuzzy subsets.