Fuzzy Galois connections on fuzzy sets
Copyright policy )Fuzzy Galois connections on fuzzy sets
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.
30 pages, final version
- Sichuan University China (People's Republic of)
- University of the Basque Country Spain
FOS: Computer and information sciences, Computer Science - Logic in Computer Science, fuzzy Galois connection, fuzzy relation, Galois correspondences, closure operators (in relation to ordered sets), quantaloid, Logic in Computer Science (cs.LO), 03B52, 06A15, 06F07, 18B35, 18D20, 18A40, preordered fuzzy set, quantale, Theory of fuzzy sets, etc., Generalizations of ordered sets
FOS: Computer and information sciences, Computer Science - Logic in Computer Science, fuzzy Galois connection, fuzzy relation, Galois correspondences, closure operators (in relation to ordered sets), quantaloid, Logic in Computer Science (cs.LO), 03B52, 06A15, 06F07, 18B35, 18D20, 18A40, preordered fuzzy set, quantale, Theory of fuzzy sets, etc., Generalizations of ordered sets
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