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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Published in | Fuzzy sets and systems Vol. 473; p. 108737 |
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Main Author | |
Format | Journal Article |
Language | English |
Published |
Elsevier B.V
15.12.2023
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Subjects | |
Online Access | Get full text |
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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. |
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ISSN: | 0165-0114 1872-6801 |
DOI: | 10.1016/j.fss.2023.108737 |