Domination of aggregation operators and preservation of transitivity

  • Authors:

  • Susanne Saminger;Radko Mesiar;Ulrich Bodenhofer

  • Affiliations:

  • Department of Algebra, Stochastics and Knowledge-Based Mathematical Systems, Johannes Kepler University, 4040 Linz, Austria;Department of Mathematics and Descriptive Geometry, Faculty of Civil Engineering, Slovak Technical University, 81 368 Bratislava, Slovakia and Institute of Theory of Information and Automation, Cz ...;Software Competence Center Hagenberg, Hauptstrasse 99, A-4232 Hagenberg, Austria

  • Venue:
  • International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems
  • Year:
  • 2002

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Abstract

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 will be 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, will be presented. Domination of isomorphic t-norms and ordinal sums of t-norms will be treated. Special attention is paid to the four basic t-norms (minimum t-norm, product t-norm, Lukasiewicz t-norm, and the drastic product).