On unification of categories associated with F -transforms and fuzzy pretopological spaces as Qua category

TL;DR

This paper introduces a new categorical framework called Qua that unifies various categories related to F-transforms and fuzzy pretopological spaces, facilitating better understanding of their relationships.

Contribution

It proposes the category Qua to unify multiple fuzzy and pretopological categories, revealing their interconnections through a common categorical structure.

Findings

Categories of fuzzy spaces are related through the new Qua category.

The framework clarifies the structure of transformations between fuzzy spaces.

Unification aids in systematic analysis of fuzzy topological concepts.

Abstract

In this contribution, our motive is to unify the categories associated with F-transforms and fuzzy pretopological spaces as a new category Qua, whose object classes are success measurements of answers and morphisms are pairs of success measurements of transformations. Specifically, the categories of spaces with L-valued fuzzy partitions, L-valued fuzzy lower transformation systems, L-valued fuzzy pretopological spaces, and Cech L-valued fuzzy interior spaces with the morphisms as pairs of L-valued fuzzy relations between the underlying sets of corresponding objects have intriguing relationships with the category Qua.