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Article
Topoi and Categories of Fuzzy Sets
Fuzzy Sets and Systems (1984)
  • Lawrence N. Stout, Illinois Wesleyan University
Abstract
Let H be a completely distributive lattice and hence a Heyting algebra. Goguen's category of fuzzy sets Set(H) Eytan's logos Fuz(H) and the topos of sheaves on H, Sh(H), are interconnected by pairs of adjoint functors between them. Each of the categories has a predicate calculus. These predicate calculi are related through the functors between the categories. Change of base lattice gives rise to several functors which preserve or reflect specific kinds of statements in the predicate calculi. This paper gives details of the categories, the predicate calculi attached to them, the functors between the categories, and the preservation properties of those functors.
Keywords
  • Fuzzy sets,
  • topoi,
  • adjoint functors.
Disciplines
Publication Date
1984
Citation Information
Lawrence N. Stout. "Topoi and Categories of Fuzzy Sets" Fuzzy Sets and Systems Vol. 12 (1984)
Available at: http://works.bepress.com/lawrence_stout/13/