Fuzzy closure operators induced by similarity

Authors:
Radim Bělohlávek
Affiliations:
Dept. Computer Science, Palacký University, Tomkova 40, CZ-779 00, Olomouc, Czech Republic and Inst. Res. Appl. Fuzzy Modeling, University of Ostrava, Bráfova 7, 701 03 Ostrava, Czech Re ...
Venue:
Fundamenta Informaticae
Year:
2003

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Abstract

In fuzzy set theory, similarity phenomenon is approached using so-called fuzzy equivalence relations. An important role in fuzzy modeling is played by similarity-based closure (called also the extensional hull). Intuitively, the degree to which an element x belongs to a similarity-based closure of a fuzzy set A is the degree to which it is true that there is an element y in A which is similar to x. In this paper, we show a basic relationship between similarity-based closure and metric closure, and provide an axiomatic characterization of the operation of a similarity-based closure.