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Transactions on Rough Sets II pp 297–318Cite as

Semantics of Fuzzy Sets in Rough Set Theory

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

Abstract

The objective of this paper is to provide a semantic framework for fuzzy sets in the theory of rough sets. Rough membership functions are viewed as a special type of fuzzy membership functions interpretable using conditional probabilities. The relationships between fuzzy membership functions and rough membership functions, between core and support of fuzzy set theory and lower and upper approximation of rough set theory, are investigated. It is demonstrated that both theories share the same qualitative properties. Interpretations of fuzzy sets in rough set theory lead to constraints on membership values. Two types of constraints on membership values are studies, namely, constraints on membership values of related elements and constraints on membership values of related sets. The classical rough set model and generalized rough set models are discussed.

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Author information

Authors and Affiliations

  1. Department of Computer Science, University of Regina, Regina, Saskatchewan, Canada, S4S 0A2

    Yiyu Yao

Authors
  1. Yiyu Yao
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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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Yao, Y. (2004). Semantics of Fuzzy Sets in Rough Set Theory. 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_15

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  • DOI: https://doi.org/10.1007/978-3-540-27778-1_15

  • 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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