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On a Generalization of the Modus Ponens: U-conditionality

  • Margalida Mas
  • Miquel Monserrat
  • Daniel Ruiz-Aguilera
  • Joan TorrensEmail author
Conference paper
Part of the Communications in Computer and Information Science book series (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.

Keywords

Fuzzy implication function Modus ponens t-norm Uninorm Natural negation 

Notes

Acknowledgments

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

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Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • Margalida Mas
    • 1
  • Miquel Monserrat
    • 1
  • Daniel Ruiz-Aguilera
    • 1
  • Joan Torrens
    • 1
    Email author
  1. 1.Department of Mathematics and Computer ScienceUniversity of the Balearic IslandsPalmaSpain

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