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Aggregating transitive fuzzy binary relations. (English) Zbl 1232.03043

Summary: We discuss the aggregation problem for transitive fuzzy binary relations. An aggregation procedure assigns a group fuzzy binary relation to each finite set of individual binary relations. Individual and group binary relations are assumed to be transitive fuzzy binary relations with respect to a given continuous t-norm. We study a particular class of aggregation procedures given by quasi-arithmetic (Kolmogorov) means and show that these procedures are well defined if and only if the t-norm is Archimedean. We also give a geometric characterization of t-norms for which the arithmetic mean is a well-defined aggregation procedure.

MSC:

03E72 Theory of fuzzy sets, etc.
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