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Rough Sets and Gradual Decision Rules

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Part of the Lecture Notes in Computer Science book series (LNAI,volume 2639)


We propose a new fuzzy rough set approach which, differently from all known fuzzy set extensions of rough set theory, does not use any fuzzy logical connectives (t-norm, t-conorm, fuzzy implication). As there is no rationale for a particular choice of these connectives, avoiding this choice permits to reduce the part of arbitrary in the fuzzy rough approximation. Another advantage of the new approach is that it is based on the ordinal property of fuzzy membership degrees only. The concepts of fuzzy lower and upper approximations are thus proposed, creating a base for induction of fuzzy decision rules having syntax and semantics of gradual rules.


  • Rough sets
  • Fuzzy sets
  • Decision rules
  • Gradual rules
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  • DOI: 10.1007/3-540-39205-X_20
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  1. Cattaneo, G., Fuzzy extension of rough sets theory, [in] L. Polkowski, A. Skowron (eds.), Rough Sets and Current Trends in Computing, LNAI 1424, Springer, Berlin 1998, pp. 275–282

    CrossRef  Google Scholar 

  2. Bouchon-Mounier, B., Yao, J., Linguistic modifiers and gradual membership to a category, International Journal on Intelligent Systems, 7 (1992) 26–36

    Google Scholar 

  3. Dubois, D., Prade, H., Gradual inference rules in approximate reasoning, Information Sciences, 61 (1992) 103–122

    CrossRef  MATH  MathSciNet  Google Scholar 

  4. Dubois, D. and Prade, H., Putting rough sets and fuzzy sets together, [in] R. SŁowiński (ed.), Intelligent Decision Support: Handbook of Applications and Advances of the Sets Theory, Kluwer, Dordrecht, 1992, pp. 203–232

    Google Scholar 

  5. Dubois, D., Prade, H., Yager, R., Information Engineering, J.Wiley, New York, 1997

    Google Scholar 

  6. Greco, S., Inuiguchi, M., SŁowiński, R., Dominance-based rough set approch using possibility and necessity measures, [in]: J.J. Alpigini, J.F. Peters, A. Skowron, N. Zhong (eds.), Rough Sets and Current Trends in Computing, Lecture Notes in Artificial Intelligence, vol. 2475, Springer-Verlag, Berlin, 2002, pp. 85–92

    CrossRef  Google Scholar 

  7. Greco, S., Matarazzo, B., Słowińskin R., The use of rough sets and fuzzy sets in MCDM. Chapter 14 [in] T. Gal, T. Stewart, T. Hanne (eds.), Advances in Multiple Criteria Decision Making, Kluwer Academic Publishers, Boston, 1999, pp. 14.1–14.59

    Google Scholar 

  8. Greco, S., Matarazzo, B., Słowiński, R., Rough set processing of vague information using fuzzy similarity relations, [in]: C.S. Calude and G. Paun (eds.), Finite Versus Infinite — Contributions to an Eternal Dilemma, Springer-Verlag, London, 2000, pp. 149–173

    Google Scholar 

  9. Greco, S., Matarazzo, B., Słowiński, R., Fuzzy extension of the rough set approach to multicriteria and multiattribute sorting, [in] J. Fodor, B. De Baets and P. Perny (eds.), Preferences and Decisions under Incomplete Knowledge, Physica-Verlag, Heidelberg, 2000, pp. 131–151

    Google Scholar 

  10. Greco, S., Matarazzo, B., Słowiński, R., Rough sets theory for multicriteria decision analysis. European J. of Operational Research 129 (2001) no. 1, 1–47

    MATH  CrossRef  Google Scholar 

  11. Greco, S., Matarazzo, B., Słowiński, R., Multicriteria classification, [in]: W. Kloesgen and J. Żytkow (eds.), Handbook of Data Mining and Knowledge Discovery, Oxford University Press, New York, 2002, chapter 16.1.9, pp. 318–328

    Google Scholar 

  12. Inuiguchi, M., Greco, S., Słowiński, R., Tanino, T., Posibility and necessity measure specification using modifiers for decision making under fuzziness, Fuzzy Sets and Systems, 2003 (to appear)

    Google Scholar 

  13. Inuiguchi, M., Tanino, T., New Fuzzy Rough Sets Based on Certainty Qualification, [in]: S. K. Pal, L. Polkowski and A. Skowron (eds.): Rough-Neuro-Computing: Techniques for Computing with Words, Springer-Verlag, Berlin, 2002

    Google Scholar 

  14. Nakamura, A., Gao, J.M., A logic for fuzzy data analysis, Fuzzy Sets and Systems, 39, 1991, 127–132

    MATH  CrossRef  MathSciNet  Google Scholar 

  15. Pawlak, Z., Rough Sets, Kluwer, Dordrecht, 1991

    MATH  Google Scholar 

  16. Polkowski, L., Rough Sets: Mathematical Foundations, Physica-Verlag, Heidelberg, 2002

    MATH  Google Scholar 

  17. Słowiński R., Rough set processing of fuzzy information, [in]: T.Y. Lin, A. Wildberger (eds.), Soft Computing: Rough Sets, Fuzzy Logic, Neural Networks, Uncertainty Management, Knowledge Discovery. Simulation Councils, Inc., San Diego, 1995, 142–145

    Google Scholar 

  18. Słowiński, R., Stefanowski, J., Rough set reasoning about uncertain data, Fundamenta Informaticae 27 (1996) 229–243

    MATH  MathSciNet  Google Scholar 

  19. Yao, Y.Y., Combination of rough and fuzzy sets based on α-level sets, [in]: T.Y. Lin and N. Cercone (eds.), Rough Sets and Data Mining: Analysis for Imprecise Data, Kluwer, Boston, 1997, pp. 301–321

    Google Scholar 

  20. Zadeh, L.A., A Fuzzy Set-Theoretic Interpretation of Linguistic Hedges, J. Cybernetics, 2 (1972) 4–34

    CrossRef  MathSciNet  Google Scholar 

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Greco, S., Inuiguchi, M., Słowiński, R. (2003). Rough Sets and Gradual Decision Rules. In: Wang, G., Liu, Q., Yao, Y., Skowron, A. (eds) Rough Sets, Fuzzy Sets, Data Mining, and Granular Computing. RSFDGrC 2003. Lecture Notes in Computer Science(), vol 2639. Springer, Berlin, Heidelberg.

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-14040-5

  • Online ISBN: 978-3-540-39205-7

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