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
Biswas, R.: On rough fuzzy sets. Bull. Polish Acad. Sci., Math, 42:351–355, 1994.
Biswas, R.: On rough sets and fuzzy rough sets. Bull. Polish Acad. Sci., Math, 42:345–349, 1994.
Dubois, D., Prade, H.: Rough fuzzy sets and fuzzy rough sets. International Journal of General Systems, 17:191–209, 1990.
Nakurnura, A.: Fuzzy rough sets. In: Note on Multiple Valued Logic in Japan, Volume 9, 1–8, 1988.
Nanda, S., Majumdar, S.: Fuzzy rough sets. Fuzzy Sets and Systems, 45:157–160, 1992.
Novotny, M., Pawlak, Z.: Characterisation of rougli top equalities and rougli bottom equalities. Bull. Polish Acad. Sci., Math, 33:91–97, 1985
Novotny, M., Pawlak, Z.: On rough equalities. Bull. Polish Acad. Sci., Math, 33:99–104, 1985
Pawlak, Z.: Rough sets, basic notations. Technical report, ICS PAS, Report 486, 1981.
Pawlak, Z.: Rough sets. International Journal of Information and Computer Science, 11:341–356, 1982.
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.
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.
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.
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”.
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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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