A top-down algorithm for generating the Hasse tree of a fuzzy preorder closure

Authors:
Bernard De Baets;Hans De Meyer;H. Naessens
Affiliations:
Dept. of Appl. Math., Ghent Univ., Gent, Belgium;-;-
Venue:
IEEE Transactions on Fuzzy Systems
Year:
2004

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Abstract

This paper describes a new top-down algorithm for the stepwise generation of the different levels or Hasse diagrams of the Hasse tree associated to the fuzzy preorder closure (min-transitive closure) of a given reflexive binary fuzzy relation. The algorithm is based upon a recently established weight-driven method for computing the min-transitive closure of a reflexive binary fuzzy relation. The way in which this method gradually establishes the fuzzy preorder closure implies that for the generation of a specific level of the Hasse tree, the newly proposed algorithm does not require the complete computation of this closure.