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Semi-divisible triangular norms

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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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Authors and Affiliations

  1. Mathematical Institute of SAS, Štefánikova 49, 81473, Bratislava, Slovakia

    A. Mesiarová-Zemánková

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  1. A. Mesiarová-Zemánková
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Correspondence to A. Mesiarová-Zemánková.

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Mesiarová-Zemánková, A. Semi-divisible triangular norms. Soft Comput 12, 535–542 (2008). https://doi.org/10.1007/s00500-007-0225-4

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  • DOI: https://doi.org/10.1007/s00500-007-0225-4

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