Aggregation of fuzzy relations and preservation of transitivity

S. Saminger, U. Bodenhofer, E. Klement, R. Mesiar. Aggregation of fuzzy relations and preservation of transitivity. volume 4342, pages 185-206, 2006.

  • Susanne Saminger
  • Ulrich Bodenhofer
  • Erich Peter Klement
  • Radko Mesiar
  • H.C.M. de Swart
  • E. Orlowska
  • M. Roubens. G. Schmidt
BuchTheory and Applications of Relationals Strucutes as Knowledge Instruments II
TypIn Sammelband
SerieLecture Notes in Computer Science
Abstract This contribution provides a comprehensive overview on the theoretical framework of aggregating fuzzy relations under the premise of preserving underlying transitivity conditions. As such it discusses the related property of dominance of aggregation operators. After a thorough introduction of all necessary and basic properties of aggregation operators, in particular dominance, the close relationship between aggregating fuzzy relations and dominance is shown. Further, principles of building dominating aggregation operators as well as classes of aggregation operators dominating one of the basic t-norms are addressed. In the paper by Bodenhofer, Küng and Saminger, also in this volume, the interested reader finds an elaborated (real world) example, i.e., an application of the herein contained theoretical framework.