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On Some Classes of RU-Implications Satisfying U-Modus Ponens

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Aggregation Functions in Theory and in Practice (AGOP 2017)

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 581))

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Abstract

The Modus Ponens property for fuzzy implication functions is essential in the inference process in approximate reasoning. It is usually considered with respect to a continuous t-norm T but it can be generalized to any conjunctor and, in particular, to a conjunctive uninorm U. In this paper, it is investigated when RU-implications derived from uninorms satisfy the Modus Ponens with respect to a conjunctive uninorm U. The new property, called here U-Modus Ponens, is studied in detail for RU-implications derived from uninorms lying in the classes of representable uninorms and uninorms continuous in the open unit square.

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Acknowledgements

This paper has been supported by the Spanish Grant TIN2016-75404-P AEI/FEDER, UE.

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Authors and Affiliations

  1. SCOPIA Research Group, Department of Mathematics and Computer Science, University of the Balearic Islands, Crta. Valldemossa, Km. 7.5, 07122, Palma, Spain

    Margarita Mas, Daniel Ruiz-Aguilera & Joan Torrens

Authors
  1. Margarita Mas
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  2. Daniel Ruiz-Aguilera
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  3. Joan Torrens
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Correspondence to Daniel Ruiz-Aguilera .

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Editors and Affiliations

  1. School of Informatics, University of Skövde, Skövde, Sweden

    Vicenç Torra

  2. Department of Mathematics and Descriptive Geometry, Slovak University of Technology, Bratislava, Slovakia

    Radko Mesiar

  3. KERMIT Research Unit Knowledge-based Systems, Ghent University, Ghent, Belgium

    Bernard De Baets

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Mas, M., Ruiz-Aguilera, D., Torrens, J. (2018). On Some Classes of RU-Implications Satisfying U-Modus Ponens. In: Torra, V., Mesiar, R., Baets, B. (eds) Aggregation Functions in Theory and in Practice. AGOP 2017. Advances in Intelligent Systems and Computing, vol 581. Springer, Cham. https://doi.org/10.1007/978-3-319-59306-7_8

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  • DOI: https://doi.org/10.1007/978-3-319-59306-7_8

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  • Print ISBN: 978-3-319-59305-0

  • Online ISBN: 978-3-319-59306-7

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