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Fuzzy sets and sheaves.: Part I -: Basic concepts
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DOI：10.1016/j.fss.2006.12.009.png)
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This essay shows that large parts of fuzzy set theory are actually subfields of sheaf theory, respectively, of the theory of complete Omega-valued sets. Hence fuzzy set theory is closer to the mainstream in mathematics than many people would expect. Part I of this essay divided into a series of two papers presents such basic concepts as Omega-valued equalities, espaces etales, singleton monad, the change of base and the subobject classifier axiom. The application of these tools to the sheaf-theoretic foundations of fuzzy sets will appear in Part II. (C) 2006 Elsevier B.V. All rights reserved.
Keyword:
category theory
Omega-valued sets
espace etale
singleton monad
complete Omega-valued sets
membership functions
geometric morphisms
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