Aggregation of fuzzy relations and preservation of transitivity

Susanne Saminger; Ulrich Bodenhofer; Erich Klement; Radko Mesiar

doi:10.1007/11964810_9

Aggregation of fuzzy relations and preservation of transitivity

Susanne Saminger
, Ulrich Bodenhofer
, Erich Klement
, Radko Mesiar

Institute for Mathematical Methods in Medicine and Data Based Modeling

Research output: Chapter in Book/Report/Conference proceeding › Conference proceedings › peer-review

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 ag$gregating 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.

Original language	English
Title of host publication	Theory and Applications of Relational Structures as Knowledge Instruments II - International Workshops of COST Action 274, TARSKI, 2002-2005, Selected Revised Papers
Editors	H. C. M. de Swart, E. Orlowska, M. Roubens, G. Schmidt
Place of Publication	Berlin Heidelberg
Publisher	Springer Verlag
Pages	185-206
Number of pages	22
ISBN (Print)	3540692231, 9783540692232
DOIs	https://doi.org/10.1007/11964810_9
Publication status	Published - 2006

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	4342 LNAI
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Fields of science

101 Mathematics
101004 Biomathematics
101027 Dynamical systems
101013 Mathematical logic
101028 Mathematical modelling
101014 Numerical mathematics
101020 Technical mathematics
101024 Probability theory
102001 Artificial intelligence
102003 Image processing
102009 Computer simulation
102019 Machine learning
102023 Supercomputing
202027 Mechatronics
206001 Biomedical engineering
206003 Medical physics
102035 Data science

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10.1007/11964810_9

Cite this

Saminger, S., Bodenhofer, U., Klement, E., & Mesiar, R. (2006). Aggregation of fuzzy relations and preservation of transitivity. In H. C. M. de Swart, E. Orlowska, M. Roubens, G. Schmidt (Ed.), Theory and Applications of Relational Structures as Knowledge Instruments II - International Workshops of COST Action 274, TARSKI, 2002-2005, Selected Revised Papers (pp. 185-206). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 4342 LNAI). Springer Verlag. https://doi.org/10.1007/11964810_9

Saminger, Susanne ; Bodenhofer, Ulrich ; Klement, Erich et al. / Aggregation of fuzzy relations and preservation of transitivity. Theory and Applications of Relational Structures as Knowledge Instruments II - International Workshops of COST Action 274, TARSKI, 2002-2005, Selected Revised Papers. editor / H. C. M. de Swart, E. Orlowska, M. Roubens, G. Schmidt. Berlin Heidelberg : Springer Verlag, 2006. pp. 185-206 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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Saminger, S, Bodenhofer, U, Klement, E & Mesiar, R 2006, Aggregation of fuzzy relations and preservation of transitivity. in H. C. M. de Swart, E. Orlowska, M. Roubens, G. Schmidt (ed.), Theory and Applications of Relational Structures as Knowledge Instruments II - International Workshops of COST Action 274, TARSKI, 2002-2005, Selected Revised Papers. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 4342 LNAI, Springer Verlag, Berlin Heidelberg, pp. 185-206. https://doi.org/10.1007/11964810_9

Aggregation of fuzzy relations and preservation of transitivity. / Saminger, Susanne; Bodenhofer, Ulrich; Klement, Erich et al.
Theory and Applications of Relational Structures as Knowledge Instruments II - International Workshops of COST Action 274, TARSKI, 2002-2005, Selected Revised Papers. ed. / H. C. M. de Swart, E. Orlowska, M. Roubens, G. Schmidt. Berlin Heidelberg: Springer Verlag, 2006. p. 185-206 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 4342 LNAI).

Research output: Chapter in Book/Report/Conference proceeding › Conference proceedings › peer-review

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Saminger S, Bodenhofer U, Klement E, Mesiar R. Aggregation of fuzzy relations and preservation of transitivity. In H. C. M. de Swart, E. Orlowska, M. Roubens, G. Schmidt, editor, Theory and Applications of Relational Structures as Knowledge Instruments II - International Workshops of COST Action 274, TARSKI, 2002-2005, Selected Revised Papers. Berlin Heidelberg: Springer Verlag. 2006. p. 185-206. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/11964810_9

Aggregation of fuzzy relations and preservation of transitivity

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