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

2025/05/05 by Abha Tripathi, Tripathi, Abha, S. P. Tiwari +1
Computer Science · Decision Sciences · #Category Theory (math.CT) #FOS: Mathematics #Fuzzy and Soft Set Theory #Rough Sets and Fuzzy Logic

paper · pdf · doi:10.48550/arxiv.2505.02535

openalex publication_date 2025/05/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• F-transforms determined by overlap and grouping maps over a complete lattice
• L-fuzzy sets
• General theory of natural equivalences

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