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A Probabilistic View of De Luca and Termini’s Entropy

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Advances in Computational Intelligence (IPMU 2012)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 298))

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Abstract

We consider two usual aspects associated to a fuzzy subset of a finite set. First, the “nonprobabilistic entropy” defined by De Luca and Termini. Second, the representation of the fuzzy set as a consonant evidence or, equivalently, as a possibility or a necessity (i. e., as a special kind of basic probability assignment or its equivalent associated fuzzy measures). Maintaining the definition of De Luca and Termini, an alternative (probabilistic) view is proposed such that it becomes a “probabilistic entropy”: the entropy of an alternative random set associated to the fuzzy set. This is a dissonant evidence, whose belief and plausibility are also characterized as special cases of fuzzy measures.

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Authors and Affiliations

  1. Dpto. de Informática y A. N., Universidad de Córdoba, Spain

    José A. Herencia

Authors
  1. José A. Herencia
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Editor information

Editors and Affiliations

  1. Faculty of Economics, University of Catania, Corso Italia, 55, 95129, Catania, Italy

    Salvatore Greco  & Benedetto Matarazzo  & 

  2. Université Pierre et Marie Curie - Paris6, CNRS UMR 7606, DAPA, LIP6 8, rue du Capitaine Scott, F-75015, Paris, France

    Bernadette Bouchon-Meunier

  3. Dip. Matematica e Informatica, Università di Perugia, 06123, Perugia, Italy

    Giulianella Coletti

  4. Department of Computer and Management Science, University of Trento, Via Inama 5, 38122, Trento, Italy

    Mario Fedrizzi

  5. Machine Intelligence Institute, IONA College, 10801, New Rochelle, NY, USA

    Ronald R. Yager

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© 2012 Springer-Verlag Berlin Heidelberg

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Herencia, J.A. (2012). A Probabilistic View of De Luca and Termini’s Entropy. In: Greco, S., Bouchon-Meunier, B., Coletti, G., Fedrizzi, M., Matarazzo, B., Yager, R.R. (eds) Advances in Computational Intelligence. IPMU 2012. Communications in Computer and Information Science, vol 298. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-31715-6_2

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  • DOI: https://doi.org/10.1007/978-3-642-31715-6_2

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-31714-9

  • Online ISBN: 978-3-642-31715-6

  • eBook Packages: Computer ScienceComputer Science (R0)

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