Fuzzy sets and sheaves. I: Basic concepts
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Publication:881818
DOI10.1016/j.fss.2006.12.009zbMath1111.18003OpenAlexW2030259157MaRDI QIDQ881818
Publication date: 18 May 2007
Published in: Fuzzy Sets and Systems (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/j.fss.2006.12.009
membership functionscategory theorygeometric morphisms\(\Omega\)-valued setscomplete \(\Omega\)-valued setsespace étalésingleton monad
Theory of fuzzy sets, etc. (03E72) Presheaves and sheaves, stacks, descent conditions (category-theoretic aspects) (18F20) Categories of sets, characterizations (18B05)
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Cites Work
- A natural interpretation of fuzzy sets and fuzzy relations
- Fuzzy relations on rings and groups
- Fuzzy normal subgroups and fuzzy cosets
- Fuzzy sets and systems. Theory and applications
- Fuzzy groups and level subgroups
- Fuzzy congruence relations
- Fuzzy normal subgroups and fuzzy quotients
- Sheaves in geometry and logic: a first introduction to topos theory
- Free fuzzy groups and fuzzy group presentations
- Fuzzy topological spaces and fuzzy compactness
- Fuzzy congruences in groups
- Membership functions for a fuzzy group from similarity relations
- Metamathematics of fuzzy logic
- Product structure of the fuzzy factor groups
- Generating fuzzy factor groups and the fundamental theorem of isomorphism
- A natural interpretation of fuzzy mappings
- L-fuzzy sets
- Fuzzy groups
- Similarity relations and fuzzy orderings
- REPRESENTATION THEOREMS FOR FUZZY CONCEPTS
- Separated Presheaves of Normed Spaces and -valued Norms
- Fuzzy sets
- AN ELEMENTARY THEORY OF THE CATEGORY OF SETS
- Fuzzy topological spaces
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