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The Relation Between F-partial Order and Distributivity Equation

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New Trends in Aggregation Theory (AGOP 2019)

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 981))

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Abstract

The notations of the order induced by triangular norms, nullnorms and uninorms have been studied widely. Nullnorms have been produced from triangular norms and triangular conorms with a zero element in the interior of the unit interval. They have been proved to be useful in several fields like expert systems, neural networks, fuzzy quantifiers. Also, the distributivity equation has been studied involving different classes of aggregation functions from triangular norms and triangular conorms to nullnorms. So, the study of the distributive property becomes very interesting, since nullnorms have been used several fields. In this paper we investigate distributivity equation for nullnorms on the unit interval [0, 1] and we give sufficient condition for two nullnorms to be equivalent.

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Acknowledgement

Second author was supported of grants VEGA 1/0006/19.

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Authors and Affiliations

  1. Department of Software Engineering, Faculty of Technology, Karadeniz Technical University, 61830, Trabzon, Turkey

    Emel Aşıcı

  2. Department of Mathematics and Descriptive Geometry, Faculty of Civil Engineering, Slovak University of Technology, Radlinského, 11, 81005, Bratislava, Slovakia

    Radko Mesiar

Authors
  1. Emel Aşıcı
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  2. Radko Mesiar
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Corresponding author

Correspondence to Emel Aşıcı .

Editor information

Editors and Affiliations

  1. Faculty of Science, Palacký University, Olomouc, Czech Republic

    Radomír Halaš

  2. Systems Research Institute, Polish Academy of Science, Warsaw, Poland

    Marek Gagolewski

  3. Slovak University of Technology, Bratislava, Slovakia

    Radko Mesiar

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Aşıcı, E., Mesiar, R. (2019). The Relation Between F-partial Order and Distributivity Equation. In: Halaš, R., Gagolewski, M., Mesiar, R. (eds) New Trends in Aggregation Theory. AGOP 2019. Advances in Intelligent Systems and Computing, vol 981. Springer, Cham. https://doi.org/10.1007/978-3-030-19494-9_10

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