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Transitive approximation of fuzzy relations by alternating closures and openings

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Abstract

 In this paper, a new method is proposed for approximating a fuzzy relation on a finite universe by a min-transitive fuzzy relation that is `close' to it. The method consists of a cascade of T-transitive closure and opening operations, where the t-norm T gradually progresses from the Lukasiewicz t-norm W to the minimum operator M. The underlying T-transitive opening heuristic is particularly interesting for t-norms T that belong to the class of copulas.

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Authors and Affiliations

  1. Department of Applied Mathematics, Biometrics and Process Control, Ghent University, Coupure links 653, B-9000 Gent, Belgium e-mail: Bernard.DeBaets@rug.ac.be, , , , , , BE

    B. De Baets

  2. Department of Applied Mathematics and Computer Science, Ghent University, Krijgslaan 281 (S9), B-9000 Gent, Belgium, , , , , , BE

    H. De Meyer

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  1. B. De Baets
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  2. H. De Meyer
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De Baets, B., De Meyer, H. Transitive approximation of fuzzy relations by alternating closures and openings. Soft Computing 7, 210–219 (2003). https://doi.org/10.1007/s00500-002-0207-5

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  • DOI: https://doi.org/10.1007/s00500-002-0207-5

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