Saminger, Susanne; Mesiar, Radko; Bodenhofer, Ulrich Domination of aggregation operators and preservation of transitivity. (English) Zbl 1053.03514 Int. J. Uncertain. Fuzziness Knowl.-Based Syst. 10, Suppl., 11-35 (2002). Summary: Aggregation processes are fundamental in any discipline where the fusion of information is of vital interest. For aggregating binary fuzzy relations such as equivalence relations or fuzzy orderings, the question arises which aggregation operators preserve specific properties of the underlying relations, e.g., \(T\)-transitivity. It is shown that preservation of \(T\)-transitivity is closely related to the domination of the applied aggregation operator over the corresponding t-norm \(T\). Furthermore, basic properties for dominating aggregation operators, not only in the case of dominating some t-norm \(T\), but dominating some arbitrary aggregation operator, are presented. Domination of isomorphic t-norms and ordinal sums of t-norms are treated. Special attention is paid to the four basic t-norms (minimum t-norm, product t-norm, Łukasiewicz t-norm, and the drastic product). Cited in 1 ReviewCited in 42 Documents MSC: 03E72 Theory of fuzzy sets, etc. 68T37 Reasoning under uncertainty in the context of artificial intelligence Keywords:domination; \(T\)-transitivity; fuzzy relations; aggregation operators PDF BibTeX XML Cite \textit{S. Saminger} et al., Int. J. Uncertain. Fuzziness Knowl.-Based Syst. 10, 11--35 (2002; Zbl 1053.03514) Full Text: DOI References: [1] Bodenhofer U., UK pp 360– (2001) [2] DOI: 10.1142/S0218488500000411 · Zbl 1113.03333 [3] Calvo T., Heidelberg pp 3– (2002) [4] DOI: 10.1142/S0218488501000727 · Zbl 1113.03335 [5] DOI: 10.1073/pnas.28.12.535 · Zbl 0063.03886 [6] DOI: 10.2140/pjm.1960.10.313 · Zbl 0091.29801 [7] Schweizer B., Publ. Math. Debrecen 8 pp 169– (1961) [8] DOI: 10.1016/S0020-0255(71)80005-1 · Zbl 0218.02058 [9] DOI: 10.1016/0165-0114(78)90012-X · Zbl 0442.68093 [10] Hohle U., Proc. EUFIT9S 1 pp 358– (1993) [11] De Baets B., J. Fuzzy Math. 5 pp 471– (1997) [12] DOI: 10.1016/S0165-0114(96)00331-4 · Zbl 0930.03070 [13] DOI: 10.1016/0020-0255(85)90045-3 · Zbl 0576.06004 [14] DOI: 10.2140/pjm.1976.65.233 · Zbl 0337.54004 [15] Riickschlossova T., Journal of Electrical Engineering 52 pp 78– (2001) [16] DOI: 10.1006/jmaa.2000.6720 · Zbl 0954.28010 [17] Mesiar R., Madrid pp 701– (2000) [18] Dubois D., Dordrecht pp 55– (1990) [19] DOI: 10.1007/BF00134116 · Zbl 0863.90020 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.