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Information Entropy and Co–entropy of Crisp and Fuzzy Granulations

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Applications of Fuzzy Sets Theory (WILF 2007)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 4578))

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Abstract

The standard approach to information entropy applied to partitions of a universe is equivalently formulated as the entropy of the corresponding crisp identity resolutions, interpreted as crisp granulations, by the corresponding characteristic functionals. Moreover, in this crisp context the co–entropy notion is introduced. The extension to the case of fuzzy identity resolutions, a particular case of fuzzy granulation, is studied.

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Author information

Authors and Affiliations

  1. Università degli Studi di Milano–Bicocca, Dipartimento di Informatica, Sistemistica e Comunicazione, Via Bicocca degli Arcimboldi 8, 20126 Milano, Italy)

    Daniela Bianucci, Gianpiero Cattaneo & Davide Ciucci

Authors
  1. Daniela Bianucci
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  2. Gianpiero Cattaneo
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  3. Davide Ciucci
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Editor information

Francesco Masulli Sushmita Mitra Gabriella Pasi

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© 2007 Springer-Verlag Berlin Heidelberg

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Bianucci, D., Cattaneo, G., Ciucci, D. (2007). Information Entropy and Co–entropy of Crisp and Fuzzy Granulations. In: Masulli, F., Mitra, S., Pasi, G. (eds) Applications of Fuzzy Sets Theory. WILF 2007. Lecture Notes in Computer Science(), vol 4578. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-73400-0_2

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  • DOI: https://doi.org/10.1007/978-3-540-73400-0_2

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-73399-7

  • Online ISBN: 978-3-540-73400-0

  • eBook Packages: Computer ScienceComputer Science (R0)

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