Fuzzy sets and geometric logic

Authors:
Steven Vickers
Affiliations:
School of Computer Science, University of Birmingham, Birmingham B15 2TT, UK
Venue:
Fuzzy Sets and Systems
Year:
2010

Citing 4
Cited 2

Topology via logic

Topology via logic
Topical categories of domains

Mathematical Structures in Computer Science
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Fuzzy sets and sheaves. Part II

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Preordered sets valued in a GL-monoid

Fuzzy Sets and Systems
Q-fuzzy subsets on ordered semigroups

Fuzzy Sets and Systems

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Abstract

Hohle has identified fuzzy sets, valued in a frame (complete Heyting algebra) @W, with certain sheaves over @W: the subsheaves of constant sheaves. More general sheaves can be got as quotients of the fuzzy sets. His principal approach to sheaves over @W, and topos-theoretic constructions on them, is via complete @W-valued sets. In this paper we show how the geometric fragment of those constructions can be described in a natural ''stalkwise'' manner, provided one works also with incomplete @W-valued sets. Our exposition examines in detail the interactions between different technical expressions of the notion of sheaf, and highlights a conceptual view of sheaf as ''continuous set-valued map''.