A Top-Down Algorithm for Generating the Hasse Tree of a Fuzzy Preorder Closure

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.