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Information Entropy and Granulation Co–Entropy of Partitions and Coverings: A Summary

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Transactions on Rough Sets X

Part of the book series: Lecture Notes in Computer Science ((TRS,volume 5656))

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Abstract

Some approaches to the covering information entropy and some definitions of orderings and quasi–orderings of coverings will be described, generalizing the case of the partition entropy and ordering. The aim is to extend to covering the general result of anti–tonicity (strictly decreasing monotonicity) of partition entropy. In particular an entropy in the case of incomplete information systems is discussed, with the expected anti-tonicity result, making use of a partial partition strategy in which the missing information is treated as a peculiar value of the system.

On the other side, an approach to generate a partition from a covering is illustrated. In particular, if we have a covering γ coarser than another covering δ with respect to a certain quasi order relation on coverings, the induced partition π(γ) results to be coarser than π(δ) with respect to the standard partial ordering on partitions. Thus, one can compare the two coverings through the entropies of the induced partitions.

The author’s work has been supported by MIUR\PRIN project “Automata and Formal languages: mathematical and application driven studies”and by “Funds of Sovvenzione Globale INGENIO allocated by Fondo Sociale Europeo, Ministero del Lavoro e della Previdenza Sociale, and Regione Lombardia”.

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Authors and Affiliations

  1. Dipartimento di Informatica, Sistemistica e Comunicazione, Università di Milano – Bicocca, Viale Sarca 336/U14, I–20126, Milano, Italia

    Daniela Bianucci & Gianpiero Cattaneo

Authors
  1. Daniela Bianucci
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  2. Gianpiero Cattaneo
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Editors and Affiliations

  1. Department of Electrical and Computer Engineering, Winnipeg, University of Manitoba, R3T 5V6, Manitoba, Canada

    James F. Peters

  2. Institute of Mathematics, Warsaw University, Banacha 2, 02-097, Warsaw, Poland

    Andrzej Skowron

  3. Department of Logic and Philosophy of Science, Maria Curie-Skłodowska University, Marii Curie-Skłodowskiej 4, 20-031, Lublin, Poland

    Marcin Wolski

  4. University of Calcutta, Kolkata, India

    Mihir K. Chakraborty

  5. Zhejiang Ocean University, Zhejiang, P.R. China

    Wei-Zhi Wu

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Bianucci, D., Cattaneo, G. (2009). Information Entropy and Granulation Co–Entropy of Partitions and Coverings: A Summary. In: Peters, J.F., Skowron, A., Wolski, M., Chakraborty, M.K., Wu, WZ. (eds) Transactions on Rough Sets X. Lecture Notes in Computer Science, vol 5656. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-03281-3_2

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  • DOI: https://doi.org/10.1007/978-3-642-03281-3_2

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-03280-6

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