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Coherent Conditional Probability, Fuzzy Inclusion and Default Rules

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Soft Computing: State of the Art Theory and Novel Applications

Part of the book series: Studies in Fuzziness and Soft Computing ((STUDFUZZ,volume 291))

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Abstract

We adopt the interpretation of fuzzy set as coherent conditional probability, and we study coherent enlargement of a probability distribution (on a random variable) and of a membership function on “fuzzy conditional events”. We consider a family of fuzzy sets closed with respect to the union and the intersection, whose membership functions are ruled by Frank t-norms and t-conorms. We study the concept of degree of fuzzy inclusion by focusing in particular on inclusion of degree 1, which can be regarded as a default rule. We get also a default logic with the relevant inference rules.

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Authors and Affiliations

  1. University of Perugia, Perugia, Italy

    Giulianella Coletti

  2. University “La Sapienza”, Rome, Italy

    Romano Scozzafava & Barbara Vantaggi

Authors
  1. Giulianella Coletti
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  2. Romano Scozzafava
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  3. Barbara Vantaggi
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Corresponding author

Correspondence to Giulianella Coletti .

Editor information

Editors and Affiliations

  1. , Iona College, Machine Intelligence Institute, New Rochelle, 10801, New York, USA

    Ronald R. Yager

  2. Information Technologies of the, Republic of Azerbaijan, Ministry of Communications and, Zarifa Aliyeva str. 33, Baku, AZ1000, Azerbaijan

    Ali M. Abbasov

  3. , Department of Electrical, University of Alberta, ECERF Building W5-023, Edmonton, T6G 2V4, Alberta, Canada

    Marek Z. Reformat

  4. , Department of Information Technology, Azerbaijan Technical University, 25 H.Cavid Ave., Baku, AZ1073, Azerbaijan

    Shahnaz N. Shahbazova

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Coletti, G., Scozzafava, R., Vantaggi, B. (2013). Coherent Conditional Probability, Fuzzy Inclusion and Default Rules. In: Yager, R., Abbasov, A., Reformat, M., Shahbazova, S. (eds) Soft Computing: State of the Art Theory and Novel Applications. Studies in Fuzziness and Soft Computing, vol 291. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-34922-5_14

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  • DOI: https://doi.org/10.1007/978-3-642-34922-5_14

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-34921-8

  • Online ISBN: 978-3-642-34922-5

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