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Generalized Modus Ponens for (U, N)-implications

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Information Processing and Management of Uncertainty in Knowledge-Based Systems. Theory and Foundations (IPMU 2018)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 853))

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Abstract

The Modus Ponens becomes an essential property in approximate reasoning and fuzzy control when forward inferences are managed. Thus, the conjunctor and the fuzzy implication function used in the inference process are required to satisfy this property. Usually, the conjunctor is modeled by a t-norm, but recently also by conjunctive uninorms. In this paper we study when (U, N)-implications satisfy the Modus Ponens property with respect to a conjunctive uninorm U in general, in a similar way as it was previously done for RU-implications. The functional inequality derived from the Modus Ponens involves in this case two different uninorms and a fuzzy negation leading to many possibilities. So, this communication presents only a first step in this study and many cases depending on the classes of the involved uninorms are worth to study.

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Notes

  1. 1.

    The subindex “cos” stands here for continuous open square.

  2. 2.

    Recall that continuous negations are the most usual ones. In particular, they contain the strong negations (those that are involutive) and also the strict ones (those that are strictly decreasing and continuous).

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Acknowledgments

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

Author information

Authors and Affiliations

  1. Department of Mathematics and Computer Science, University of the Balearic Islands, 07122, Palma, Balearic Islands, Spain

    M. Mas, D. Ruiz-Aguilera & Joan Torrens

  2. Balearic Islands Health Research Institute (IdISBa), 07010, Palma, Spain

    M. Mas, D. Ruiz-Aguilera & Joan Torrens

Authors
  1. M. Mas
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  2. D. Ruiz-Aguilera
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  3. Joan Torrens
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Corresponding author

Correspondence to D. Ruiz-Aguilera .

Editor information

Editors and Affiliations

  1. Universidad de Cádiz, Cádiz, Cadiz, Spain

    Jesús Medina

  2. Universidad de Málaga, Málaga, Málaga, Spain

    Manuel Ojeda-Aciego

  3. Universidad de Granada, Granada, Spain

    José Luis Verdegay

  4. Universidad de Granada, Granada, Spain

    David A. Pelta

  5. Universidad de Málaga, Málaga, Málaga, Spain

    Inma P. Cabrera

  6. LIP6, Université Pierre et Marie Curie, CNRS, Paris, France

    Bernadette Bouchon-Meunier

  7. Iona College, New Rochelle, New York, USA

    Ronald R. Yager

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Mas, M., Ruiz-Aguilera, D., Torrens, J. (2018). Generalized Modus Ponens for (U, N)-implications. In: Medina, J., et al. Information Processing and Management of Uncertainty in Knowledge-Based Systems. Theory and Foundations. IPMU 2018. Communications in Computer and Information Science, vol 853. Springer, Cham. https://doi.org/10.1007/978-3-319-91473-2_55

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  • DOI: https://doi.org/10.1007/978-3-319-91473-2_55

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  • Print ISBN: 978-3-319-91472-5

  • Online ISBN: 978-3-319-91473-2

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