Fuzzy closure operators induced by similarity

  • Authors:

  • Radim Belohlávek

  • Affiliations:

  • Dept. Computer Science, Palacky University, Olomouc, Czech Republic and Inst. Res. Appl. Fuzzy Modeling, University of Ostrava, Ostrava, Czech Republic

  • Venue:
  • IFSA'03 Proceedings of the 10th international fuzzy systems association World Congress conference on Fuzzy sets and systems
  • 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 give an axiomatic characterization of the operation of a similarity-based closure and discuss some consequences and related topics.