Author:
Mustafa Demirci
Affiliation:
Akdeniz University and Faculty of Sciences, Turkey
Keyword(s):
Fuzzy Set, Fuzzy Logic, Fuzzy Topology, Quantale, Semi-Quantale, Category Theory, Adjoint Situation, Equivalence, Spatiality, Sobriety.
Related
Ontology
Subjects/Areas/Topics:
Artificial Intelligence
;
Computational Intelligence
;
Fuzzy Systems
;
Mathematical Foundations: Fuzzy Set Theory and Fuzzy Logic
;
Soft Computing
Abstract:
The present paper introduces M-fuzzy semi-quantales, fuzzifying semi-quantales, and (L,M)-quasi-fuzzy
topological spaces, providing a common framework for (L,M)-fuzzy topological spaces of Kubiak and Sostak, ˇ
L-quasi-fuzzy topological spaces of Rodabaugh and L-fuzzy topological spaces of Hohle and ¨ Sostak. In this ˇ
paper, we set up a dual adjunction between the category of (L,M)-quasi-fuzzy topological spaces and the
category of M-fuzzy semi-quantales, and then show that this adjunction includes a dual equivalence between
the category of (L,M)-sober (L,M)-quasi-fuzzy topological spaces and the category of (L,M)-spatial M-fuzzy
semi-quantales.