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On a Generalization of the Modus Ponens: U-conditionality

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Information Processing and Management of Uncertainty in Knowledge-Based Systems (IPMU 2016)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 610))

Abstract

In fuzzy logic, the Modus Ponens property for fuzzy implication functions is usually considered with respect to a continuous t-norm T and for this reason this property is also known under the name of T-conditionality. In this paper, the t-norm T is substituted by a uninorm U leading to the property of U-conditionality. The new property is studied in detail and it is shown that usual implications derived from t-norms and t-conorms do not satisfy it, but many solutions appear among those implications derived from uninorms. In particular, the case of residual implications derived from uninorms or RU-implications is investigated in detail for some classes of uninorms.

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Acknowledgments

This paper has been partially supported by the Spanish grant TIN2013-42795-P.

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Authors and Affiliations

  1. Department of Mathematics and Computer Science, University of the Balearic Islands, Crta. de Valldemossa, km. 7,5, 07122, Palma, Spain

    Margalida Mas, Miquel Monserrat, Daniel Ruiz-Aguilera & Joan Torrens

Authors
  1. Margalida Mas
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  2. Miquel Monserrat
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  3. Daniel Ruiz-Aguilera
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  4. Joan Torrens
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Corresponding author

Correspondence to Joan Torrens .

Editor information

Editors and Affiliations

  1. INESC-ID,Instituto Superior Técnico, Universidade de Lisboa, Lisboa, Portugal

    Joao Paulo Carvalho

  2. LIP 6, Université Pierre et Marie Curie, Paris, France

    Marie-Jeanne Lesot

  3. School of Industrial Engineering, Eindhoven University of Technology, Eindhoven, The Netherlands

    Uzay Kaymak

  4. IDMEC,Instituto Superior Técnico, Universidade de Lisboa, Lisboa, Portugal

    Susana Vieira

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

    Bernadette Bouchon-Meunier

  6. Machine Intelligence Institute, Iona College, New Rochelle, New York, USA

    Ronald R. Yager

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Mas, M., Monserrat, M., Ruiz-Aguilera, D., Torrens, J. (2016). On a Generalization of the Modus Ponens: U-conditionality. In: Carvalho, J., Lesot, MJ., Kaymak, U., Vieira, S., Bouchon-Meunier, B., Yager, R. (eds) Information Processing and Management of Uncertainty in Knowledge-Based Systems. IPMU 2016. Communications in Computer and Information Science, vol 610. Springer, Cham. https://doi.org/10.1007/978-3-319-40596-4_33

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  • DOI: https://doi.org/10.1007/978-3-319-40596-4_33

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-40595-7

  • Online ISBN: 978-3-319-40596-4

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