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Annual Conference of the Japanese Society for Artificial Intelligence

JSAI 2001: New Frontiers in Artificial Intelligence pp 295–300Cite as

On Rough Sets under Generalized Equivalence Relations

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Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 2253))

Abstract

We consider two generalized situations: a case when an equivalence relation is generalized to a similarity relation and a case when a partition is generalized to a cover. Two interpretations of rough sets, i.e., the approximation by means of elementary sets and the distinction among positive, negative and boundary regions, are conceivable. The relations between two generalized situations are investigated. Rough sets are generalized based on two different interpretations under two different situations. Fundamental properties and complete definability are discussed in each generalization.

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References

  1. Bonikowski, Z., Bryniarski, E., Wybraniec-Skardowska, U.: Extensions and Intensions in the Rough Set Theory. Information Sciences 107 (1998) 149–167

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  3. Inuiguchi, M., Tanino, T.: Fuzzy Rough Sets Based on Certainty Qualifications. Proceedings of the Forth Asian Fuzzy Systems Symposium 1 (2000) 433–438

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  4. Słowinski, R., Vanderpooten, D.: A Generalized Definition of Rough Approximations Based on Similarity. IEEE Transactions on Data and Knowledge Engineering 12(2) (2000) 331–336

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Author information

Authors and Affiliations

  1. Department of Electronics and Information Systems, Graduate School of Engineering, Osaka University, 2-1, Yamada-Oka, 565-0871, Suita, Osaka, Japan

    Masahiro Inuiguchi & Tetsuzo Tanino

Authors
  1. Masahiro Inuiguchi
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  2. Tetsuzo Tanino
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Editor information

Editors and Affiliations

  1. Graduate School of Business Science, The University of Tsukuba, Tokyo

    Takao Terano  & Yukio Ohsawa  & 

  2. School of Engineering, The University of Tokyo, Tokyo

    Toyoaki Nishida

  3. Dept.of Computer Science, National Defense Academy, Japan

    Akira Namatame

  4. School of Medicines, Shimane Medical University, Japan

    Syusaku Tsumoto

  5. The Institute of Scientific and Industrial Research, Osaka University, Osaka

    Takashi Washio

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© 2001 Springer-Verlag Berlin Heidelberg

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Cite this paper

Inuiguchi, M., Tanino, T. (2001). On Rough Sets under Generalized Equivalence Relations. In: Terano, T., Ohsawa, Y., Nishida, T., Namatame, A., Tsumoto, S., Washio, T. (eds) New Frontiers in Artificial Intelligence. JSAI 2001. Lecture Notes in Computer Science(), vol 2253. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45548-5_34

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  • DOI: https://doi.org/10.1007/3-540-45548-5_34

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-43070-4

  • Online ISBN: 978-3-540-45548-6

  • eBook Packages: Springer Book Archive

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