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On Axiomatic Characterizations of Fuzzy Approximation Operators

I. The Fuzzy Rough Set Based Case

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Rough Sets and Current Trends in Computing (RSCTC 2000)

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Abstract

In a previous paper we have developed an axiomatic characterization of approximation operators defined by the classical diamond and box operator of modal logic. The paper presented contains the analogous results of approximation operators which are denned by using the concepts of fuzzy rough sets.

This research was supported by the Deutche Forschungsgemeinschaft as part of the Colaborrative Research Center “Computational Intelligence(531)”

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References

  1. Biswas, R.: On rough fuzzy sets. Bull. Polish Acad. Sci., Math, 42:351–355, 1994.

    MATH  MathSciNet  Google Scholar 

  2. Biswas, R.: On rough sets and fuzzy rough sets. Bull. Polish Acad. Sci., Math, 42:345–349, 1994.

    MATH  MathSciNet  Google Scholar 

  3. Dubois, D., Prade, H.: Rough fuzzy sets and fuzzy rough sets. International Journal of General Systems, 17:191–209, 1990.

    Article  MATH  Google Scholar 

  4. Nakurnura, A.: Fuzzy rough sets. In: Note on Multiple Valued Logic in Japan, Volume 9, 1–8, 1988.

    Google Scholar 

  5. Nanda, S., Majumdar, S.: Fuzzy rough sets. Fuzzy Sets and Systems, 45:157–160, 1992.

    Article  MATH  MathSciNet  Google Scholar 

  6. Novotny, M., Pawlak, Z.: Characterisation of rougli top equalities and rougli bottom equalities. Bull. Polish Acad. Sci., Math, 33:91–97, 1985

    MATH  MathSciNet  Google Scholar 

  7. Novotny, M., Pawlak, Z.: On rough equalities. Bull. Polish Acad. Sci., Math, 33:99–104, 1985

    MATH  MathSciNet  Google Scholar 

  8. Pawlak, Z.: Rough sets, basic notations. Technical report, ICS PAS, Report 486, 1981.

    Google Scholar 

  9. Pawlak, Z.: Rough sets. International Journal of Information and Computer Science, 11:341–356, 1982.

    Article  MathSciNet  MATH  Google Scholar 

  10. Thiele, H.: On the definitions of modal operators in fuzzy-logic. In: 23rd International Symposium on Multiple-Valued Logic, 62–67, Sacramento, California, May 24-27, 1993.

    Google Scholar 

  11. Thiele, H.: Fuzzy rough sets versus rough fuzzy sets-an interpretation and a comparative study using concepts of modal logics. In: 5th European Congress on Intelligent Techniques and Soft Computing (EUFIT’97), Volume l, 159–167, Aachen, Germany, September 8-11, 1997.

    Google Scholar 

  12. Thiele, H.: On Closure Operators in Fuzzy Deductive Systems and Fuzzy Algebras. Paper, 28th International Symposium on Multiple-Valued Logic, Proceedings, 304–309, Fukuoka, Japan, May 27-29, 1998. Extended Version: On Closure Operators in FiJK/y Algebras and Fu/zy Deductive Systems. Technical Report CI-34/98, 23 pages, University ofDortmund, Collaborative Research (center 531 (Computational Intelligence), April 1998.

    Google Scholar 

  13. Thiele, H.: On Axiomatic Characterisations of Crisp Approximation Operators. Paper, 7th International Conference on Fuzzy Theory and Technology, Proceedings56–59, Atlantic City, New Jersey, USA, February 27-March 3, 2000. To be published in “Information Sciences”.

    Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Computer Science I, University of Dortmund, D-44221, Dortmund, Germany

    Helmut Thiele

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  1. Helmut Thiele
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Editor information

Editors and Affiliations

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

    Wojciech Ziarko  & Yiyu Yao  & 

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Thiele, H. (2001). On Axiomatic Characterizations of Fuzzy Approximation Operators. In: Ziarko, W., Yao, Y. (eds) Rough Sets and Current Trends in Computing. RSCTC 2000. Lecture Notes in Computer Science(), vol 2005. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45554-X_33

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  • DOI: https://doi.org/10.1007/3-540-45554-X_33

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-43074-2

  • Online ISBN: 978-3-540-45554-7

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