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On Idempotent n-ary Uninorms

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Modeling Decisions for Artificial Intelligence (MDAI 2019)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 11676))

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Abstract

In this paper we describe the class of idempotent n-ary uninorms on a given chain. When the chain is finite, we axiomatize the latter class by means of the following conditions: associativity, quasitriviality, symmetry, and nondecreasing monotonicity. Also, we show that associativity can be replaced with bisymmetry in this new axiomatization.

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Notes

  1. 1.

    This paper is also an extended version of [7].

  2. 2.

    When \(X=X_k\) for some integer \(k\ge 1\), the graphical representation of \(f_{\preceq }\) is then obtained by joining the points \((1,1),\ldots ,(k,k)\) by line segments.

  3. 3.

    To simplify the representation of the connected components, we omit edges that can be obtained by transitivity.

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Acknowledgments

The first author is supported by the Luxembourg National Research Fund under the project PRIDE 15/10949314/GSM. The second author is also supported by the Hungarian National Foundation for Scientific Research, Grant No. K124749.

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Authors and Affiliations

  1. University of Luxembourg, Mathematics Research Unit, Esch-sur-Alzette, Luxembourg

    Jimmy Devillet & Jean-Luc Marichal

  2. Hungarian Academy of Sciences, Alfréd Rényi Institute of Mathematics, Budapest, Hungary

    Gergely Kiss

Authors
  1. Jimmy Devillet
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  2. Gergely Kiss
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  3. Jean-Luc Marichal
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Corresponding author

Correspondence to Jimmy Devillet .

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Editors and Affiliations

  1. Maynooth University, Maynooth, Ireland

    Vicenç Torra

  2. Tamagawa University, Machida, Tokyo, Japan

    Yasuo Narukawa

  3. University of Milano-Bicocca, Milan, Italy

    Gabriella Pasi

  4. University of Milano-Bicocca, Milan, Italy

    Marco Viviani

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Devillet, J., Kiss, G., Marichal, JL. (2019). On Idempotent n-ary Uninorms. In: Torra, V., Narukawa, Y., Pasi, G., Viviani, M. (eds) Modeling Decisions for Artificial Intelligence. MDAI 2019. Lecture Notes in Computer Science(), vol 11676. Springer, Cham. https://doi.org/10.1007/978-3-030-26773-5_9

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  • DOI: https://doi.org/10.1007/978-3-030-26773-5_9

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-26772-8

  • Online ISBN: 978-3-030-26773-5

  • eBook Packages: Computer ScienceComputer Science (R0)

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