Ovchinnikov, Sergei Aggregating transitive fuzzy binary relations. (English) Zbl 1232.03043 Int. J. Uncertain. Fuzziness Knowl.-Based Syst. 3, No. 1, 47-55 (1995). 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. Cited in 3 Documents MSC: 03E72 Theory of fuzzy sets, etc. Keywords:aggregation procedure; quasi-arithmetic mean; T-transitivity PDFBibTeX XMLCite \textit{S. Ovchinnikov}, Int. J. Uncertain. Fuzziness Knowl.-Based Syst. 3, No. 1, 47--55 (1995; Zbl 1232.03043) Full Text: DOI