The dominance relation on the class of continuous ordinal sum t-norms

Susanne Saminger; Peter Sarkoci; Bernard De Baets

The dominance relation on the class of continuous ordinal sum t-norms

Susanne Saminger
, Peter Sarkoci
, Bernard De Baets

Institute for Mathematical Methods in Medicine and Data Based Modeling

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

Abstract

This paper addresses the relation of dominance on the class of continuous t-norms with a particular focus on continuous ordinal sum t-norms. Exactly, in this framework counter-examples to the conjecture that dominance is not only a reﬂexive and antisymmetric, but also a transitive relation could be found. We elaborate the details which have led to these results and illustrate them by several examples. In addition, to this original and comprehensive overview, we provide geometrical insight into dominance relationships involving prototypical Archimedean t-norms, the Lukasiewicz t-norm and the product t-norm.

Original language	English
Title of host publication	Theory and Applications of Relational Structures as Knowledge Instruments II
Editors	H. C. M. de Swart, E. Orlowska, M. Roubens, G. Schmidt
Place of Publication	Berlin Heidelberg
Publisher	Springer Verlag
Pages	334-354
Number of pages	21
Publication status	Published - 2006

Publication series

Name	Lecture Notes in Computer Science (LNCS)

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

Cite this

Saminger, Susanne ; Sarkoci, Peter ; De Baets, Bernard. / The dominance relation on the class of continuous ordinal sum t-norms. Theory and Applications of Relational Structures as Knowledge Instruments II. editor / H. C. M. de Swart, E. Orlowska, M. Roubens, G. Schmidt. Berlin Heidelberg : Springer Verlag, 2006. pp. 334-354 (Lecture Notes in Computer Science (LNCS)).

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The dominance relation on the class of continuous ordinal sum t-norms. / Saminger, Susanne; Sarkoci, Peter; De Baets, Bernard.
Theory and Applications of Relational Structures as Knowledge Instruments II. ed. / H. C. M. de Swart, E. Orlowska, M. Roubens, G. Schmidt. Berlin Heidelberg: Springer Verlag, 2006. p. 334-354 (Lecture Notes in Computer Science (LNCS)).

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

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AU - Sarkoci, Peter

AU - De Baets, Bernard

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AB - This paper addresses the relation of dominance on the class of continuous t-norms with a particular focus on continuous ordinal sum t-norms. Exactly, in this framework counter-examples to the conjecture that dominance is not only a reﬂexive and antisymmetric, but also a transitive relation could be found. We elaborate the details which have led to these results and illustrate them by several examples. In addition, to this original and comprehensive overview, we provide geometrical insight into dominance relationships involving prototypical Archimedean t-norms, the Lukasiewicz t-norm and the product t-norm.

M3 - Chapter

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BT - Theory and Applications of Relational Structures as Knowledge Instruments II

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