Fuzzy Galois connections on fuzzy sets
arXiv:1707.08849 · doi:10.1016/j.fss.2018.05.016
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.
30 pages, final version
References in corpus (7)
- Categorical structures enriched in a quantaloid: categories, distributors and functors
- Categorical structures enriched in a quantaloid: tensored and cotensored categories
- Topological categories, quantaloids and Isbell adjunctions
- -closure spaces
- Yoneda completeness and flat completeness of ordered fuzzy sets
- Fixed points of adjoint functors enriched in a quantaloid
- Limits and colimits of quantaloid-enriched categories and their distributors