5 research outputs found
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.Comment: 30 pages, final versio
Quantaloidal Completions of Order-enriched Categories and Their Applications
By introducing the concept of quantaloidal completions for an order-enriched
category, relationships between the category of quantaloids and the category of
order-enriched categories are studied. It is proved that quantaloidal
completions for an order-enriched category can be fully characterized as
compatible quotients of the power-set completion. As applications, we show that
a special type of injective hull of an order-enriched category is the MacNeille
completion; the free quantaloid over an order-enriched category is the Down-set
completion