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arXiv · 1707.08849

Fuzzy Galois connections on fuzzy sets

Javier Gutiérrez García·Hongliang Lai·Lili Shen
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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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Javier Gutiérrez García, Hongliang Lai, Lili Shen. 2017-07-27. Fuzzy Galois connections on fuzzy sets. https://doi.org/10.1016/j.fss.2018.05.016

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