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Cuts of IF-sets Respecting Fuzzy Connectives

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Fuzzy Logic and Applications (WILF 2011)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 6857))

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Abstract

Intuitionistic fuzzy sets (IF-sets) are a suitable tool to describe cases where it is useful to account not only the grade of membership to a collection, but also the grade of its non-membership. We consider the α-cuts of an IF-set A as crisp sets consisting of those elements x for which the truth value (in fuzzy logic) of the statement ”x belongs to A and it is not true that x does not belong to A” is at least α. We describe properties of such cuts depending on the chosen type of conjunction and negation.

The research in this paper is partly supported by the Internationalization Plan 2010 of the University of Oviedo, the Foundation for the promotion in Asturias of the scientific and technologic research grant BP10-090, by the Agency of the Slovak Ministry of Education for the Structural Funds of the EU, under project ITMS:26220120007 and the Spanish Ministry of Science and Innovation grant MTM2010-17844.

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Author information

Authors and Affiliations

  1. Department of Statistics and O.R., University of Oviedo, Spain

    Davide Martinetti & Susana Montes

  2. Department of Mathematics, Faculty of Natural Sciences, Matej Bel University, Slovak Republic

    Vladimír Janiš

Authors
  1. Davide Martinetti
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  2. Vladimír Janiš
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  3. Susana Montes
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Editor information

Editors and Affiliations

  1. Computer Science Department, University of Bari, Via E. Orabona, 4, 70125, Bari, Italy

    Anna Maria Fanelli

  2. Department of Electrical and Computer Engineering, University of Alberta, T6G 2V4, Edmonton, Alberta, Canada

    Witold Pedrycz

  3. Department of Apllied Science, University of Naples Parthenope, Centro Direzionale Is. C4, 80143, Naples, Italy

    Alfredo Petrosino

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© 2011 Springer-Verlag Berlin Heidelberg

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Martinetti, D., Janiš, V., Montes, S. (2011). Cuts of IF-sets Respecting Fuzzy Connectives. In: Fanelli, A.M., Pedrycz, W., Petrosino, A. (eds) Fuzzy Logic and Applications. WILF 2011. Lecture Notes in Computer Science(), vol 6857. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-23713-3_5

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  • DOI: https://doi.org/10.1007/978-3-642-23713-3_5

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-23712-6

  • Online ISBN: 978-3-642-23713-3

  • eBook Packages: Computer ScienceComputer Science (R0)

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