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Rough Mereology as a Link between Rough and Fuzzy Set Theories. A Survey

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Transactions on Rough Sets II

Part of the book series: Lecture Notes in Computer Science ((TRS,volume 3135))

Abstract

In this paper, we discuss rough inclusions defined in Rough Mereology – a paradigm for approximate reasoning introduced by Polkowski and Skowron – as a basis for common models for rough as well as fuzzy set theories. We justify the point of view that tolerance (or, similarity) is the motif common to both theories. To this end, we demonstrate in Sect. 6 that rough inclusions (which represent a hierarchy of tolerance relations) induce rough set theoretic approximations as well as partitions and equivalence relations in the sense of fuzzy set theory. Before that, we include an account of mereological theory in Sect. 3. We also discuss granulation mechanisms based on rough inclusions with an outline of applications to rough–fuzzy–neurocomputing and computing with words in Sects. 4 and 5.

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Authors and Affiliations

  1. Polish Japanese Institute of Information Technology, Koszykowa 86, 02 008, Warsaw, Poland

    Lech Polkowski

  2. Dept. Math.Computer Science, Univ. Warmia and Mazury, Zolnierska 14 A, 10 561, Olsztyn, Poland

    Lech Polkowski

Authors
  1. Lech Polkowski
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Editor information

Editors and Affiliations

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

    James F. Peters

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

    Andrzej Skowron

  3. Institut de Recherche en Informatique de Toulouse, France

    Didier Dubois

  4. Institute of Computer Science, Polish Academy of Sciences, 01–237, Warsaw, Poland

    Jerzy W. Grzymała-Busse

  5. Department of Systems Innovation, Graduate School of Engineering Science, Osaka University, 1-3, Machikaneyama, Toyonaka, 560-8531, Osaka, Japan

    Masahiro Inuiguchi

  6. Polish-Japanese Institute of Information Technology Warsaw, Poland Department of Mathematics and Computer Science, University of Warmia and Mazury, Olsztyn, Poland

    Lech Polkowski

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© 2004 Springer-Verlag Berlin Heidelberg

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Polkowski, L. (2004). Rough Mereology as a Link between Rough and Fuzzy Set Theories. A Survey. In: Peters, J.F., Skowron, A., Dubois, D., Grzymała-Busse, J.W., Inuiguchi, M., Polkowski, L. (eds) Transactions on Rough Sets II. Lecture Notes in Computer Science, vol 3135. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-27778-1_13

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  • DOI: https://doi.org/10.1007/978-3-540-27778-1_13

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-23990-1

  • Online ISBN: 978-3-540-27778-1

  • eBook Packages: Computer ScienceComputer Science (R0)

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