Generalizations of Rough Sets: From Crisp to Fuzzy Cases

  • Masahiro Inuiguchi
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3066)


Rough sets can be interpreted in two ways: classification of objects and approximation of a set. In this paper, we discuss the differences and similarities of generalized rough sets based on those two different interpretations. We describe the relations between generalized rough sets and types of extracted decision rules. Moreover, we extend the discussion to fuzzy rough sets. Through this paper, the relations among generalized crisp rough sets and fuzzy rough sets are clarified and two different directions of applications in rule extraction are suggested.


Decision Rule Extensive Relation Granular Computing Conceivable Region Fuzzy Case 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. 1.
    Alpigini, J.J., Peters, J.F., Skowron, A., Zhong, N.: RSCTC 2002. LNCS (LNAI), vol. 2475. Springer, Heidelberg (2002)zbMATHCrossRefGoogle Scholar
  2. 2.
    Bonikowski, Z., Bryniarski, E., Wybraniec-Skardowska, U.: Extensions and Intensions in the Rough Set Theory. Information Sciences 107, 149–167 (1998)zbMATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    Dubois, D., Prade, H.: Rough Fuzzy Sets and Fuzzy Rough Sets. Int. J. General Syst. 17, 191–209 (1990)zbMATHCrossRefGoogle Scholar
  4. 4.
    Dubois, D., Prade, H.: Putting Rough Sets and Fuzzy Sets Together. In: Słowiński, R. (ed.) Intelligent Decision Support, pp. 203–232. Kluwer, Dordrecht (1992)Google Scholar
  5. 5.
    Greco, S., Inuiguchi, M., Słowiński, R.: Rough Sets and Gradual Decision Rules. In: Wang, G., et al. (eds.) Rough Sets, Fuzzy Sets, Data Mining, and Granular Computing, pp. 156–164. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  6. 6.
    Greco, S., Matarazzo, B., Słowiński, R.: The Use of Rough Sets and Fuzzy Sets in MCDM. In: Gal, T., Stewart, T.J., Hanne, T. (eds.) Multicriteria Decision Making: Advances in MCDM Models, Algorithms, Theory, and Applications, pp. 1451–1459. Kluwer Academic Publishers, Boston (1999)Google Scholar
  7. 7.
    Inuiguchi, M.: Two Generalizations of Rough Sets and Their Fundamental Properties. In: Proceedings of 6th Workshop on Uncertainty Processing, Hejnice, Czech Republic, September 24-27, pp. 113–124 (2003)Google Scholar
  8. 8.
    Inuiguchi, M.: Classification-versus Approximation-oriented Fuzzy Rough Sets. In: Proceedings of IPMU 2004, Perugia, Italy, July 4-9 (2004)Google Scholar
  9. 9.
    Inuiguchi, M., Hirano, S., Tsumoto, S.: Rough Set Theory and Granular Computing. Springer, Berlin (2003)zbMATHGoogle Scholar
  10. 10.
    Inuiguchi, M., Tanino, T.: Two Directions toward Generalization of Rough Sets. In: Inuiguchi, M., Hirano, S., Tsumoto, S. (eds.) Rough Set Theory and Granular Computing, pp. 47–57. Springer, Berlin (2003)Google Scholar
  11. 11.
    Inuiguchi, M., Tanino, T.: New Fuzzy Rough Sets Based on Certainty Qualification. In: Pal, K., Polkowski, L., Skowron, A. (eds.) Rough-Neural Computing, pp. 278–296. Springer, Heidelberg (2003)Google Scholar
  12. 12.
    Inuiguchi, M., Tanino, T.: Function Approximation by Fuzzy Rough Sets. In: Bouchon-Meunier, B., Foulloy, L., Yager, R.R. (eds.) Intelligent Systems for Information Processing: From Representation to Applications, pp. 93–104. Elsevier, Amsterdam (2003)Google Scholar
  13. 13.
    Pawlak, Z.: Rough Sets: Theoretical Aspects of Reasoning About Data. Kluwer Academic Publishers, Boston (1991)zbMATHGoogle Scholar
  14. 14.
    Słowiński, R., Vanderpooten, D.: A Generalized Definition of Rough Approximations Based on Similarity. IEEE Transactions on Data and Knowledge Engineering 12(2), 331–336 (2000)CrossRefGoogle Scholar
  15. 15.
    Wang, G., Liu, Q., Yao, Y., Skowron, A.: RSFDGrC 2003. LNCS (LNAI), vol. 2639. Springer, Heidelberg (2003)zbMATHCrossRefGoogle Scholar
  16. 16.
    Yao, Y.Y.: Two Views of the Theory of Rough Sets in Finite Universes. International Journal of Approximate Reasoning 15, 291–317 (1996)zbMATHCrossRefMathSciNetGoogle Scholar
  17. 17.
    Yao, Y.Y.: Relational Interpretations of Neighborhood Operators and Rough Set Approximation Operators. Information Sciences 111, 239–259 (1998)zbMATHCrossRefMathSciNetGoogle Scholar
  18. 18.
    Yao, Y.Y., Lin, T.Y.: Generalization of Rough Sets Using Modal Logics. Intelligent Automation and Soft Computing 2(2), 103–120 (1996)Google Scholar
  19. 19.
    Ziarko, W.: Variable Precision Rough Set Model. J. Comput. Syst. Sci. 46(1), 39–59 (1993)zbMATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Masahiro Inuiguchi
    • 1
  1. 1.Department of Systems Innovation, Graduate School of Engineering ScienceOsaka UniversityOsakaJapan

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