Domination of aggregation operators and preservation of transitivity

S. Saminger, R. Mesiar, U. Bodenhofer. Domination of aggregation operators and preservation of transitivity. Internat. J. Uncertainty, Fuzziness, Knowledge-Based Systems, volume 10, pages 11-35, 2002.

  • Susanne Saminger
  • Radko Mesiar
  • Ulrich Bodenhofer
JournalInternat. J. Uncertainty, Fuzziness, Knowledge-Based Systems
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 specificproperties of the underlying relations, e.g. T-transitivity. It will be shown that preservationof T-transitivity is closely related to the domination of the applied aggregation operator overthe 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 aggregationoperator, will be presented. Domination of isomorphic t-norms and ordinal sums of t-normswill be treated. Special attention is paid to the four basic t-norms (minimum t-norm, productt-norm, Lukasiewicz t-norm, and the drastic product).