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A comparison of two types of rough sets induced by coverings. (English) Zbl 1191.68689
Summary: Rough set theory is an important technique in knowledge discovery in databases. In covering-based rough sets, many types of rough set models were established in recent years. In this paper, we compare the covering-based rough sets defined by Zhu with ones defined by Xu and Zhang. We further explore the properties and structures of these types of rough set models. We also consider the reduction of coverings. Finally, the axiomatic systems for the lower and upper approximations defined by Xu and Zhang are constructed.

MSC:
68T37 Reasoning under uncertainty in the context of artificial intelligence
68T30 Knowledge representation
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[1] Bonikowski, Z.; Bryniarski, E.; Wybraniec, U., Extensions and intentions in the rough set theory, Information sciences, 107, 149-167, (1998) · Zbl 0934.03069
[2] Chen, D.; Zhang, W.; Yeung, D.; Tsang, E., Rough approximations on a complete completely distributive lattice with applications to generalized rough sets, Information sciences, 176, 1829-1848, (2006) · Zbl 1104.03053
[3] Chen, D.; Wang, C.; Hu, Q., A new approach to attribute reduction of consistent and inconsistent covering decision systems with covering rough sets, Information sciences, 177, 3500-3518, (2007) · Zbl 1122.68131
[4] Dai, J.H., Rough 3-valued algebras, Information sciences, 178, 1986-1996, (2008) · Zbl 1134.06008
[5] Dubois, D.; Prade, H., Rough fuzzy sets and fuzzy rough sets, International journal of general systems, 17, 191-209, (1990) · Zbl 0715.04006
[6] Eric, C.C.T.; Chen, D.; Yeung, D.S., Approximations and reducts with covering generalized rough sets, Computers and mathematics with applications, 56, 279-289, (2008) · Zbl 1145.68547
[7] Kelley, J.L., General topology, Graduate texts in mathematics, vol. 27, (1955), Springer-Verlag · Zbl 0066.16604
[8] Kondo, M., Algebraic approach to generalized rough sets, Lecture notes in artificial intelligence, 3641, 132-140, (2005) · Zbl 1134.68509
[9] Kondo, M., On the structure of generalized rough sets, Information sciences, 176, 589-600, (2006) · Zbl 1096.03065
[10] Li, T.J.; Leung, Y.; Zhang, W.X., Generalized fuzzy rough approximation operators based on fuzzy coverings, International journal of approximate reasoning, 48, 3, 836-856, (2008) · Zbl 1186.68464
[11] Liu, G.L., The axiomatization of the rough set upper approximation operations, Fundamenta informaticae, 69, 331-342, (2006) · Zbl 1096.68150
[12] Liu, G.L., Generalized rough sets over fuzzy lattices, Information sciences, 178, 1651-1662, (2008) · Zbl 1136.03328
[13] Liu, G.L., Axiomatic systems for rough sets and fuzzy rough sets, International journal of approximate reasoning, 48, 857-867, (2008) · Zbl 1189.03056
[14] Liu, G.L.; Zhu, W., The algebraic structures of generalized rough set theory, Information sciences, 178, 4105-4113, (2008) · Zbl 1162.68667
[15] Mi, J.S.; Zhang, W.X., An axiomatic characterization of a fuzzy generalization of rough sets, Information sciences, 160, 235-249, (2004) · Zbl 1041.03038
[16] Pawlak, Z., Rough sets, International journal of computer and information sciences, 11, 341-356, (1982) · Zbl 0501.68053
[17] Pawlak, Z., Rough sets: theoretical aspects of reasoning about data, (1991), Kluwer Academic Publishers Boston · Zbl 0758.68054
[18] Pawlak, Z.; Skowron, A., Rudiments of rough sets, Information sciences, 177, 1, 3-27, (2007) · Zbl 1142.68549
[19] Pawlak, Z.; Skowron, A., Rough sets: some extensions, Information sciences, 177, 1, 28-40, (2007) · Zbl 1142.68550
[20] Pawlak, Z.; Skowron, A., Rough sets and Boolean reasoning, Information sciences, 177, 1, 41-73, (2007) · Zbl 1142.68551
[21] Qi, G.; Liu, W., Rough operations on Boolean algebras, Information sciences, 173, 49-63, (2005) · Zbl 1074.03025
[22] Radzikowska, A.M.; Kerre, E.E., A comparative study of fuzzy rough sets, Fuzzy sets and systems, 126, 137-155, (2002) · Zbl 1004.03043
[23] A.M. Radzikowska, E.E. Kerre, Fuzzy rough sets based on residuated lattices, in: Transactions on Rough Sets, vol. 3135, LNCS, 2004, pp. 278-296. · Zbl 1109.68118
[24] Skowron, A.; Stepaniuk, J., Tolerance approximation spaces, Fundamenta informaticae, 27, 245-253, (1996) · Zbl 0868.68103
[25] Slowinski, R.; Vanderpooten, D., A generalized definition of rough approximations based on similarity, IEEE transactions on knowledge and data engineering, 12, 2, 331-336, (1990)
[26] Wu, W.Z.; Mi, J.S.; Zhang, W.X., Generalized fuzzy rough sets, Information sciences, 151, 263-282, (2003) · Zbl 1019.03037
[27] Wu, W.Z.; Zhang, W.X., Constructive and axiomatic approaches of fuzzy approximation operators, Information sciences, 159, 233-254, (2004) · Zbl 1071.68095
[28] Wu, W.Z.; Leung, Y.; Mi, J.S., On characterizations of (I, T)-fuzzy rough approximation operators, Fuzzy sets and systems, 154, 76-102, (2005) · Zbl 1074.03027
[29] W.Z. Wu, W.X. Zhang, Rough set approximations vs. measurable spaces, in: IEEE International Conference on Granular Computing, 2006, pp. 329-332.
[30] Xu, W.H.; Zhang, W.X., Measuring roughness of generalized rough sets induced by a covering, Fuzzy sets and systems, 158, 2443-2455, (2007) · Zbl 1127.68106
[31] J.T. Yao, A ten-year review of granular computing, in: Proceedings of 2007 IEEE International Conference on Granular Computing, 2007, pp. 734-739.
[32] Yao, Y.Y., Two views of the theory of rough sets in finite universes, International journal of approximate reasoning, 15, 291-317, (1996) · Zbl 0935.03063
[33] Yao, Y.Y., Relational interpretations of neighborhood operators and rough set approximation operators, Information sciences, 111, 1-4, 239-259, (1998) · Zbl 0949.68144
[34] Yao, Y.Y., Constructive and algebraic methods of theory of rough sets, Information sciences, 109, 21-47, (1998) · Zbl 0934.03071
[35] Yao, Y.Y.; Lin, T.Y., Generalization of rough sets using modal logic, Intelligent automation and soft computing, an international journal, 2, 103-120, (1996)
[36] Zhang, H.; Liang, H.; Liu, D., Two new operators in rough set theory with applications to fuzzy sets, Information sciences, 166, 1-4, 147-165, (2004) · Zbl 1101.68871
[37] Zhu, W.; Wang, F.Y., Reduction and axiomization of covering generalized rough sets, Information sciences, 152, 217-230, (2003) · Zbl 1069.68613
[38] Zhu, W., Topological approaches to covering rough sets, Information sciences, 177, 6, 1499-1508, (2007) · Zbl 1109.68121
[39] Zhu, W.; Wang, F.Y., On three types of covering rough sets, IEEE transactions on knowledge and data engineering, 19, 8, 1131-1144, (2007)
[40] Zhu, W., Generalized rough sets based on relations, Information sciences, 177, 22, 4997-5011, (2007) · Zbl 1129.68088
[41] Zhu, W., Relationship between generalized rough sets based on binary relation and covering, Information sciences, 179, 210-225, (2009) · Zbl 1163.68339
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