Fuzzy Galois connections on fuzzy sets
Javier Guti\'errez Garc\'ia, Hongliang Lai, Lili Shen
TL;DR
This paper develops a theoretical framework for preordered fuzzy sets using enriched category theory, focusing on fuzzy Galois connections and their foundational properties within a purely order-theoretic context.
Contribution
It introduces a novel order-theoretic approach to quantale-valued preorders and fuzzy Galois connections, bridging fuzzy set theory with enriched category theory.
Findings
Establishment of quantale-valued preorders on fuzzy sets
Development of fuzzy Galois connections within this framework
Purely order-theoretic formulation for fuzzy set theory
Abstract
In fairly elementary terms this paper presents how the theory of preordered fuzzy sets, more precisely quantale-valued preorders on quantale-valued fuzzy sets, is established under the guidance of enriched category theory. Motivated by several key results from the theory of quantaloid-enriched categories, this paper develops all needed ingredients purely in order-theoretic languages for the readership of fuzzy set theorists, with particular attention paid to fuzzy Galois connections between preordered fuzzy sets.
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