On the existence and construction of T-transitive closures

  • Authors:
  • B. De Baets;H. De Meyer

  • Affiliations:
  • Department of Applied Mathematics, Biometrics and Process Control, Ghent University, Coupure links 653, B-9000 Gent, Belgium;Department of Applied Mathematics and Computer Science, Ghent University, Krijgslaan 281 (S9), B-9000 Gent, Belgium

  • Venue:
  • Information Sciences: an International Journal
  • Year:
  • 2003

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Abstract

In this paper, it is shown that any fuzzy relation R on an arbitrary universe X has a T - transitive closure. The triangular norm T involved is not subject to any conditions. This existential result can be turned into an explicit expression in the case of a left-continuous triangular norm T . Furthermore, this continuity restriction vanishes in the case of a finite universe X . In that case, the explicit expression can also be operationalized.