Aggregation of fuzzy relations and preservation of transitivity

Authors Susanne Saminger
Ulrich Bodenhofer
Erich Peter Klement
Radko Mesiar
Editors H.C.M. de Swart
E. Orlowska
M. Roubens. G. Schmidt
Title Aggregation of fuzzy relations and preservation of transitivity
Booktitle Theory and Applications of Relationals Strucutes as Knowledge Instruments II
Type in collection
Publisher Springer
Series Lecture Notes in Computer Science
Volume 4342
Department IDM
ISBN 3-540-69223-1
Year 2006
Pages 185-206
SCCH ID# 605
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.