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Interval-valued fuzzy relations in a set structures. (English) Zbl 0874.04003

If \(X\) and \(Y\) are two sets, an interval-valued fuzzy relation on \(X\times Y\) is an interval-valued fuzzy set of \(X\times Y\), that is a fuzzy set whose membership function has values in a closed subinterval of \([0,1]\). The authors define the concepts of identity, symmetry, antisymmetry, reflexivity and antireflexivity based on triangular norms and conorms. Some particular relations defined on \(X\times X\) are called relations of order because they induce a particular ordering on the referential set \(X\). Many properties are established.
Reviewer: A.Di Nola (Napoli)

MSC:

03E72 Theory of fuzzy sets, etc.
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