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Semi-divisible triangular norms

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A. Mesiarová-ZemánkováAuthors Info & Claims

Soft Computing - A Fusion of Foundations, Methodologies and Applications, Volume 12, Issue 6

Pages 535 - 542

Published: 01 April 2008 Publication History

Abstract

Semi-divisibility of left-continuous triangular norms is a weakening of the divisibility (i.e., continuity) axiom for t-norms. In this contribution we focus on the class of semi-divisible t-norms and show the following properties: Each semi-divisible t-norm with Ran(n _T) = [0, 1] is nilpotent. Semi-divisibility of an ordinal sum t-norm is determined by the corresponding property of its first component (which can be a proper t-subnorm, too). Finally, negations with finite range derived from semi-divisible t-norms are studied.

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Index Terms

Semi-divisible triangular norms
1. Mathematics of computing
  1. Mathematical analysis
    1. Numerical analysis
2. Theory of computation

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cover image Soft Computing - A Fusion of Foundations, Methodologies and Applications

Soft Computing - A Fusion of Foundations, Methodologies and Applications Volume 12, Issue 6

April 2008

92 pages

ISSN:1432-7643

EISSN:1433-7479

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Springer-Verlag

Berlin, Heidelberg

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Published: 01 April 2008

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Abstract

References

Index Terms

Recommendations

Structure of left-continuous triangular norms with strong induced negations: (III) construction and decomposition

On ordinal sums of triangular norms on bounded lattices

Semi-divisible t-norms on discrete scales

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