Domination of aggregation operators and preservation of transitivity

Susanne Saminger, Radko Mesiar, Ulrich Bodenhofer

Research output: Contribution to journalArticlepeer-review

92 Citations (Scopus)

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).

Original languageEnglish
Pages (from-to)11-35
Number of pages25
JournalInternational Journal of Uncertainty, Fuzziness and Knowlege-Based Systems
Volume10
Issue numberSupplement
DOIs
Publication statusPublished - Dec 2002

Keywords

  • Aggregation operators
  • Domination
  • Fuzzy relations
  • T-transitivity

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