Quantale-valued convex structures as lax algebras

Based on a unital and commutative quantale (Q,⁎), a Q-valued lax extension of the nonempty finite powerset monad and a Q-valued finitary closure space (also called algebraic Q-valued closure space) are introduced. It is proved that the category of (Pf,Q)-categories with respect to the Q-valued lax e...

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Bibliographic Details
Published inFuzzy sets and systems Vol. 473; p. 108737
Main Author Pang, Bin
Format Journal Article
LanguageEnglish
Published Elsevier B.V 15.12.2023
Subjects
Balaced Q-convex structure
Fuzzy convex structure
Lax algebra
Monad
Q-fuzzifying convex structure
Q-fuzzifying convex structure
Balaced Q-convex structure
Fuzzy convex structure
Monad
Lax algebra
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Summary:Based on a unital and commutative quantale (Q,⁎), a Q-valued lax extension of the nonempty finite powerset monad and a Q-valued finitary closure space (also called algebraic Q-valued closure space) are introduced. It is proved that the category of (Pf,Q)-categories with respect to the Q-valued lax extension of the nonempty finite powerset monad Pf is isomorphic to that of Q-valued finitary closure spaces. Considering the Q-valued finitary closure spaces as linkages, it is shown that balanced Q-convex structures can be treated as (Pf,Q)-categories when Q is required to be a frame and Q-fuzzifying convex structures can be treated as (Pf,Q)-categories when Q is required to be a completely distributive De Morgan algebra.
ISSN:0165-0114
1872-6801
DOI:10.1016/j.fss.2023.108737