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A new approach to attribute reduction of consistent and inconsistent covering decision systems with covering rough sets. (English) Zbl 1122.68131

Summary: Traditional rough set theory is mainly used to extract rules from and reduce attributes in databases in which attributes are characterized by partitions, while the covering rough set theory, a generalization of traditional rough set theory, does the same yet characterizes attributes by covers. In this paper, we propose a way to reduce the attributes of covering decision systems, which are databases characterized by covers. First, we define consistent and inconsistent covering decision systems and their attribute reductions. Then, we state the sufficient and the necessary conditions for reduction. Finally, we use a discernibility matrix to design algorithms that compute all the reducts of consistent and inconsistent covering decision systems. Numerical tests on four public data sets show that the proposed attribute reductions of covering decision systems accomplish better classification performance than those of traditional rough sets.

MSC:

68T37 Reasoning under uncertainty in the context of artificial intelligence
68T30 Knowledge representation

Software:

UCI-ml
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[1] C.L. Blake, C.J. Merz, UCI Repository of machine learning databases, Tech. Rep., Univ. California, Dept. Inform. Comp. Sci., Irvine, CA. Available from: <http://www.ics.uci.edu/mlearn/MachineLearning.html>, 1998.
[2] Bonikowski, Z.; Bryniarski, E.; Wybraniec, U., Extensions and intentions in the rough set theory, Information sciences, 107, 149-167, (1998) · Zbl 0934.03069
[3] Bonikowski, Z., Algebraic structures of rough sets, (), 243-247 · Zbl 0819.04009
[4] Bryniarski, E., A calculus of rough sets of the first order, Bulletin of the Polish Academy of sciences, 16, 71-77, (1989) · Zbl 0756.04002
[5] Cattaneo, G., Abstract approximate spaces for rough theories, (), 59-98 · Zbl 0927.68087
[6] Degang, Chen; Wenxiu, Zhang; Yeung, S.; Tsang, C.C., Rough approximations on a complete completely distributive lattice with applications to generalized rough sets, Information sciences, 176, 1829-1848, (2006) · Zbl 1104.03053
[7] Fernandez Salido, J.M.; Murakami, S., Rough set analysis of a general type of fuzzy data using transitive aggregations of fuzzy similarity relations, Fuzzy sets and systems, 139, 635-660, (2003) · Zbl 1047.68139
[8] Hu, Q.H.; Yu, D.R.; Xie, Z.X., Information-preserving hybrid data reduction based on fuzzy-rough techniques, Pattern recognition letters, 27, 5, 414-423, (2006)
[9] Hu, Q.H.; Li, X.D.; Yu, D.R., Analysis on classification performance of rough set based reducts, (), 423-433
[10] Kryszkiewicz, M., Rough set approach to incomplete information systems, Information sciences, 112, 39-49, (1998) · Zbl 0951.68548
[11] Kryszkiewicz, M., Rule in incomplete information systems, Information sciences, 113, 271-292, (1999) · Zbl 0948.68214
[12] T.Y. Lin, Neighborhood systems and relational database, in: Proceeding of CSC’88, 1988, p. 725.
[13] Lin, T.Y., Neighborhood systems-application to qualitative fuzzy and rough sets, (), 132-155
[14] Lin, T.Y.; Lin, Q.; Huang, K.J.; Chen, W., Rough sets, neighborhood systems and application, (), 130-141
[15] T.Y. Lin, Y.Y. Yao, Mining soft rules using rough sets and neighborhoods, in: Proceedings of CESA’96, IMASCS Multiconference, Lille, France, July 9-12, 1996, pp. 1095-1100.
[16] Mordeson, J.N., Rough set theory applied to (fuzzy) ideal theory, Fuzzy sets and systems, 121, 315-324, (2001) · Zbl 1030.68085
[17] H.S. Nguyen, D. Slezak, Approximation reducts and association rules correspondence and complexity results, in: N. Zhong, A. Skowron, S. Oshuga (Eds.), Proceedings of RSFDGrC’99, Yamaguchi, Japan. LNAI1711, 1999, pp. 137-145. · Zbl 0954.68129
[18] Pawlak, Z., Rough sets, International journal of computer and information sciences, 11, 341-356, (1982) · Zbl 0501.68053
[19] Pawlak, Z., Rough sets: theoretical aspects of reasoning about data, (1991), Kluwer Academic Publishing Dordrecht · Zbl 0758.68054
[20] Pawlak, Z.; Skowron, Andrzej, Rudiments of rough sets, Information sciences, 177, 3-27, (2006) · Zbl 1142.68549
[21] Pawlak, Z.; Skowron, Andrzej, Rough sets: some extensions, Information sciences, 177, 28-40, (2006) · Zbl 1142.68550
[22] Pawlak, Z.; Skowron, Andrzej, Rough sets and Boolean reasoning, Information sciences, 177, 41-73, (2006) · Zbl 1142.68551
[23] Pomykala, J.A., Approximation operations in approximation space, Bulletin of the Polish Academy of sciences, 9-10, 653-662, (1987) · Zbl 0642.54002
[24] Skowron, A.; Stepaniuk, J., Tolerance approximation spaces, Fundamenta informaticae, 27, 245-253, (1996) · Zbl 0868.68103
[25] Skowron, A.; Rauszer, C., The discernibility matrices and functions in information systems, ()
[26] Slowinski, R.; Vanderpooten, D., A generalized definition of rough approximations based on similarity, IEEE transactions data knowledge engineering, 2, 331-336, (2000)
[27] Wasilewska, A., Topological rough algebras, (), 411-425 · Zbl 0860.03042
[28] Yao, Y.Y., Constructive and algebraic method of theory of rough sets, Information sciences, 109, 21-47, (1998) · Zbl 0934.03071
[29] Yao, Y.Y., Relational interpretations of neighborhood operators and rough set approximation operators, Information sciences, 101, 239-259, (1998) · Zbl 0949.68144
[30] Zakowski, W., Approximations in the space \((\text{U,} \operatorname{\Pi})\), Demonstratio Mathematica, 16, 761-769, (1983) · Zbl 0553.04002
[31] Ziarko, W., Variable precision rough set model, Journal of computer and system sciences, 46, 39-59, (1993) · Zbl 0764.68162
[32] Zhang, W.-X.; Wu, W.-Z.; Liang, J.-Y.; Li, D.-Y., Theory and method of rough sets, (2001), Science Press Beijing
[33] Zhu, William; Wang, Fei-Yue, Some results on the covering generalized rough sets, Pattern recognition artificial intelligence, 5, 6-13, (2002)
[34] Zhu, William; Wang, Fei-Yue, Reduction and axiomization of covering generalized rough sets, Information sciences, 152, 217-230, (2003) · Zbl 1069.68613
[35] Zhu, William, Topological approaches to covering rough sets, Information sciences, 177, 1892-1915, (2007)
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