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Weak Implication and Fuzzy Inclusion

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Preferences and Decisions

Part of the book series: Studies in Fuzziness and Soft Computing ((STUDFUZZ,volume 257))

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Abstract

The content of this talk is taken from joint papers with G. Coletti and B. Vantaggi.

We define weak implication \(H\longmapsto_P E\) (“H weakly implies E under P”) through the relation P(E|H) = 1, where P is a (coherent) conditional probability.

In particular (as a ... by-product) we get “inferential rules”, that correspond to those of default logic. We discuss also connections between weak implication and fuzzy inclusion.

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References

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Author information

Authors and Affiliations

  1. Dip. Metodi e Modelli Matematici, University “La Sapienza”, Via Scarpa 16, 00161, Roma, Italy

    Romano Scozzafava

Authors
  1. Romano Scozzafava
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Editor information

Editors and Affiliations

  1. Department of Economics and Quantitative Methods, University of Catania, Corso Italia 55, 95129, Catania, Italy

    Salvatore Greco

  2. Department of Computer and Management Sciences, University of Trento, Via Inama 5, 38122, Trento, Italy

    Ricardo Alberto Marques Pereira

  3. Department of Economical and Social Sciences, University of Sannio at Benevento, Via delle Puglie, 82100, Benevento, Italy

    Massimo Squillante

  4. Machine Intelligence Institute, Iona College, 10801, New Rochelle, NY, USA

    Ronald R. Yager

  5. Systems Research Institute, Polish Academy of Sciences, ul. Newelska 6, 01–447, Warsaw, Poland

    Janusz Kacprzyk

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Scozzafava, R. (2010). Weak Implication and Fuzzy Inclusion. In: Greco, S., Marques Pereira, R.A., Squillante, M., Yager, R.R., Kacprzyk, J. (eds) Preferences and Decisions. Studies in Fuzziness and Soft Computing, vol 257. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-15976-3_23

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  • DOI: https://doi.org/10.1007/978-3-642-15976-3_23

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-15975-6

  • Online ISBN: 978-3-642-15976-3

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