Aggregation of fuzzy relations and preservation of transitivity

Authors:
Susanne Saminger;Ulrich Bodenhofer;Erich Peter Klement;Radko Mesiar
Affiliations:
Department of Knowledge-Based Mathematical Systems, Johannes Kepler University, Linz, Austria;Institute of Bioinformatics, Johannes Kepler University, Linz, Austria;Department of Knowledge-Based Mathematical Systems, Johannes Kepler University, Linz, Austria;Department of Mathematics and Descriptive Geometry, Faculty of Civil Engineering, Slovak University of Technology, Bratislava, Slovakia
Venue:
TARSKI'02-05 Proceedings of the 2006 international conference on Theory and Applications of Relational Structures as Knowledge Instruments - Volume 2
Year:
2006

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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.