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Uninorms and Nullnorms and their Idempotent Versions on Bounded Posets

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Modeling Decisions for Artificial Intelligence (MDAI 2019)

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

Abstract

The paper deals with uninorms and nullnorms as basic operations which are associative, commutative and monotone (increasing). These operations were first introduced on the unit interval and later generalized to bounded lattices. In this contribution we show how it is possible to generalize them to bounded posets. We will study their existence, property and conditions under which it is possible to construct their idempotent versions, since these are the most important operations from the point of view of possible applications.

Supported by the VEGA grant agency, grant No. 2/0069/16 and 1/0006/19, and by the Science and Technology Assistance Agency under contract No. APVV-18-0052.

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Authors and Affiliations

  1. Faculty of Civil Engineering, Slovak University of Technology, Radlinského 11, Sk-810 05, Bratislava, Slovakia

    Martin Kalina

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  1. Martin Kalina
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Correspondence to Martin Kalina .

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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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Kalina, M. (2019). Uninorms and Nullnorms and their Idempotent Versions on Bounded Posets. 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_12

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  • DOI: https://doi.org/10.1007/978-3-030-26773-5_12

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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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