DocumentCode
2542971
Title
Fuzzy sets, sheaves, and topoi
Author
Barone, Joseph M.
Author_Institution
Datatek Corp., Bridgewater, NJ, USA
fYear
2000
fDate
2000
Firstpage
456
Lastpage
460
Abstract
There have been a number of attempts to provide a categorical foundation for fuzzy sets. One inescapable limitation seems to be that fuzzy sets cannot form a topos without restrictions placed on the underlying lattice or on the associated “equality”. This paper reviews work in this area and concludes that categorical unification of fuzzy sets, at least of the kinds described to date, may be unnecessary and even inappropriate given the varieties of “real-world” semantics that fuzzy set theory needs to support
Keywords
category theory; fuzzy set theory; categorical unification; category theory; fuzzy set theory; lattice; real world semantics; sheaves; topoi; topos; Algebra; Electrostatic precipitators; Fuzzy logic; Fuzzy set theory; Fuzzy sets; Lattices; Pulleys; Uncertainty;
fLanguage
English
Publisher
ieee
Conference_Titel
Fuzzy Information Processing Society, 2000. NAFIPS. 19th International Conference of the North American
Conference_Location
Atlanta, GA
Print_ISBN
0-7803-6274-8
Type
conf
DOI
10.1109/NAFIPS.2000.877473
Filename
877473
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