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Reduction and axiomization of covering generalized rough sets. (English) Zbl 1069.68613
Summary: This paper investigates some basic properties of covering generalized rough sets, and their comparison with the corresponding ones of Pawlak’s rough sets, a tool for data mining. The focus here is on the concepts and conditions for two coverings to generate the same covering lower approximation or the same covering upper approximation. The concept of reducts of coverings is introduced and the procedure to find a reduct for a covering is given. It has been proved that the reduct of a covering is the minimal covering that generates the same covering lower approximation or the same covering upper approximation, so this concept is also a technique to get rid of redundancy in data mining. Furthermore, it has been shown that covering lower and upper approximations determine each other. Finally, a set of axioms is constructed to characterize the covering lower approximation operation.

MSC:
68T37Reasoning under uncertainty
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References:
[1] Bonikowski, Z.; Bryniarski, E.; Wybraniec, U.: Extensions and intentions in the rough set theory. Inform. sci. 107, 149-167 (1998) · Zbl 0934.03069
[2] Bonikowski, Z.: Algebraic structures of rough sets. Rough sets, fuzzy sets and knowledge discovery (1994) · Zbl 0819.04009
[3] Bryniaski, E.: A calculus of rough sets of the first order. Bull. Pol acad. Sci. 16, 71-77 (1989)
[4] Cattaneo, G.: Abstract approximation spaces for rough theories. Rough sets in knowledge discovery 1: methodology and applications (1998) · Zbl 0927.68087
[5] Lin, T.; Liu, Q.: Rough approximate operators: axiomatic rough set theory. Rough sets, fuzzy sets and knowledge discovery (1994) · Zbl 0818.03028
[6] Pawlak, Z.: Rough sets, theoretical aspects of reasoning about data. (1991) · Zbl 0758.68054
[7] Pomykala, J. A.: Approximation operations in approximation space. Bull. Pol acad. Sci. 9--10, 653-662 (1987)
[8] Skowron, A.; Stepaniuk, J.: Tolerance approximation spaces. Fundam. inform. 27, 245-253 (1996) · Zbl 0868.68103
[9] Slowinski, R.; Vanderpooten, D.: A generalized definition of rough approximations based on similarity. IEEE trans. Data knowledge eng. 2, 331-336 (2000)
[10] Wasilewska, A.: Topological rough algebras. Rough sets & data mining (1997) · Zbl 0860.03042
[11] F. Wang, Modeling, analysis and synthesis of linguistic dynamic systems: a computational theory, in: Proceedings of IEEE International Workshop on Architecture for Semiotic Modeling and Situation Control in Large Complex Systems, Monterery, CA, 27--30 August 1995, pp. 173--178
[12] Wang, F.: Outline of a computational theory for linguistic dynamic systems: toward computing with words. Int. J. Intell. contr. Syst. 2, 211-224 (1998)
[13] Yao, Y. Y.: Relational interpretations of neighborhood operators and rough set approximation operators. Inform. sci. 101, 239-259 (1998) · Zbl 0949.68144
[14] Yao, Y. Y.: Constructive and algebraic methods of theory of rough sets. Inform. sci. 109, 21-47 (1998) · Zbl 0934.03071
[15] Zadeh, L. A.: Fuzzy sets. Inform. contr. 8, 338-353 (1965) · Zbl 0139.24606
[16] Zadeh, L. A.: The concept of a linguistic variable and its application to approximate reasoning----I, II, III. Inform. sci. 8, No. 9, 199-249 (1975) · Zbl 0397.68071
[17] Zadeh, L. A.: Fuzzy logic=computing with words. IEEE trans. Fuzzy syst. 4, 103-111 (1996)
[18] Zakowski, W.: Approximations in the space (U, \prod). Demonstratio Mathematica 16, 761-769 (1983)
[19] Zhu, F.; He, H.: Logical properties of rough sets. Proceedings of the fourth international conference on high performance computing in the Asia-Pacific region, 670-671 (2000)
[20] Zhu, F.; He, H.: The axiomization of the rough set. Chinese J. Comput. 23, 330-333 (2000)
[21] F. Zhu, On covering generalized rough sets, MS thesis, The University of Arizona, Tucson, Arizona, USA, May, 2002
[22] Zhu, F.; Wang, F.: Some results on covering generalized rough sets. Pattern recog. Artificial intell. 15, 6-13 (2002)