Aggregation of Fuzzy Relations and Preservation of Transitivity

  • Susanne Saminger
  • Ulrich Bodenhofer
  • Erich Peter Klement
  • Radko Mesiar
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4342)


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.


Aggregation Operator Fuzzy Relation Triangular Norm Fuzzy Equivalence Relation Binary Fuzzy Relation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Susanne Saminger
    • 1
  • Ulrich Bodenhofer
    • 2
  • Erich Peter Klement
    • 1
  • Radko Mesiar
    • 3
    • 4
  1. 1.Department of Knowledge-Based Mathematical SystemsJohannes Kepler UniversityLinzAustria
  2. 2.Institute of BioinformaticsJohannes Kepler UniversityLinzAustria
  3. 3.Department of Mathematics and Descriptive GeometryFaculty of Civil Engineering, Slovak University of TechnologyBratislavaSlovakia
  4. 4.Institute for Research and Applications of Fuzzy ModelingUniversity of OstravaOstrava 1Czech Republic

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