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Residual Implications from Discrete Uninorms. A Characterization

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Enric Trillas: A Passion for Fuzzy Sets

Part of the book series: Studies in Fuzziness and Soft Computing ((STUDFUZZ,volume 322))

Abstract

The operators defined on a finite chain, usually called discrete operators, constitute a field of increasing interest because of their applications to qualitative aggregation and computing with words. We introduce in this paper the residual implications derived from discrete uninorms, we look at their most interesting properties and their axiomatic characterization is also given.

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Acknowledgments

It was our pleasure to jointly work with Professor Enric Trillas in some aspects of fuzzy implication functions. We would like to bring him this work with our respect and admiration. This paper has been partially supported by the Spanish Grants MTM2009-10320 and TIN2013-42795-P, both with FEDER support.

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Authors and Affiliations

  1. Department of Mathematics and Computer Science, University of the Balearic Islands Cra, Valldemossa Km 7.5, 07122, Palma de Mallorca, Spain

    Margarita Mas, Gaspar Mayor, Miquel Monserrat & Joan Torrens

Authors
  1. Margarita Mas
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  2. Gaspar Mayor
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  3. Miquel Monserrat
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  4. Joan Torrens
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Corresponding author

Correspondence to Joan Torrens .

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Editors and Affiliations

  1. European Centre for Soft Computing, Asturias, Spain

    Luis Magdalena

  2. Depto. de Ciencias de la Computación e Inteligencia Artificial, University of Granada, Granada, Spain

    Jose Luis Verdegay

  3. Spanish Council for Scientific Research (CSIC), Artificial Intelligence Research Institute (IIIA-CSIC), Catalonia, Spain

    Francesc Esteva

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Mas, M., Mayor, G., Monserrat, M., Torrens, J. (2015). Residual Implications from Discrete Uninorms. A Characterization. In: Magdalena, L., Verdegay, J., Esteva, F. (eds) Enric Trillas: A Passion for Fuzzy Sets. Studies in Fuzziness and Soft Computing, vol 322. Springer, Cham. https://doi.org/10.1007/978-3-319-16235-5_3

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  • DOI: https://doi.org/10.1007/978-3-319-16235-5_3

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-16234-8

  • Online ISBN: 978-3-319-16235-5

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