Algorithms for the computation of T-transitive closures

Authors:
H. Naessens;H. De Meyer;B. De Baets
Affiliations:
Hogeschool Gent;-;-
Venue:
IEEE Transactions on Fuzzy Systems
Year:
2002

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Abstract

We present two weight-driven algorithms for the computation of the T-transitive closure of a symmetric binary fuzzy relation on a finite universe X with cardinality n (or, equivalently, of a symmetric (n×n)-matrix with elements in [0, 1]), with T a triangular norm. The first algorithm is proven to be valid for any triangular norm T, whereas the second algorithm is shown to be valid when T is either the minimum operator or an Archimedean triangular norm. Furthermore, we investigate how these algorithms can be appropriately adapted to generate the T-transitive closure of nonsymmetric binary fuzzy relations (or matrices) as well.