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On fuzzy monotone convergence Q-cotopological spaces
- Source :
- Fuzzy Sets and Systems. 425:18-33
- Publication Year :
- 2021
- Publisher :
- Elsevier BV, 2021.
-
Abstract
- In this paper, we generalize the concept of a monotone convergence space (also called a d-space) to the setting of a Q -cotopological space, where Q is a commutative and integral quantale. We establish a D-completion for every stratified Q -cotopological space, which is a category reflection of the category S Q -CTop of stratified Q -cotopological spaces onto the full subcategory S Q -DCTop of monotone convergence Q -cotopological spaces. By introducing the notion of a tapered set, a direct characterization of the completion is obtained: the D-completion of each stratified Q -cotopological space X consists exactly of those tapered closed sets in X. We show that the D-completion can be applied to obtain a universal fuzzy directed completion of a Q -ordered set by endowing it with the Scott cotopology, taking the D-completion, and then passing to the specialization Q -order. Consequently, the category Q -DOrd of fuzzy directed complete Q -ordered sets and Scott continuous functions is reflective in the category Q -OrdĪ of Q -ordered sets and Scott continuous functions.
- Subjects :
- Subcategory
0209 industrial biotechnology
Closed set
Logic
Quantale
02 engineering and technology
Characterization (mathematics)
Space (mathematics)
Fuzzy logic
Combinatorics
020901 industrial engineering & automation
Monotone polygon
Artificial Intelligence
0202 electrical engineering, electronic engineering, information engineering
020201 artificial intelligence & image processing
Commutative property
Mathematics
Subjects
Details
- ISSN :
- 01650114
- Volume :
- 425
- Database :
- OpenAIRE
- Journal :
- Fuzzy Sets and Systems
- Accession number :
- edsair.doi...........1d9fbb35b1fc0eb37101192af89787d6