Research on Relative Reducts of Rough Set Model in Consistent and Inconsistent Decision Tables

Abstract:

Z. Pawlak’s classical rough set theory has been widely applied in analyzing ordinary information systems and decision tables. In this theory, a relative reduct can be considered as a minimum set of attributes that preserves a certain classification property. This paper investigates three different classification properties, and proposes three distinct definitions accordingly. According to the three classification properties, we can define three distinct definitions respectively. Based on the common structure of the specific definitions of relative reducts and discernibility matrices, general definitions of relative reducts and discernibility matrices are suggested.

• Periodical: Applied Mechanics and Materials (Volumes 644-650)
• Pages: 1590-1606
• DOI: https://doi.org/10.4028/www.scientific.net/AMM.644-650.1590
• Online since: September 2014
• Authors: Tao Yan*, Chong Zhao Han
• Keywords: Attribute Reduction, Consistent, Inconsistent Decision Tables, Rough Set Theory

References

[1] Z. Pawlak, Rough sets, International Journal of Computer and Information Sciences 11 (1982), p.341–356.

[2] Q.H. Hu, Z.X. Xie, D.R. Yu, Hybrid attribute reduction based on a novel fuzzy-rough model and information granulation, Pattern Recognition Letters 40 (2007), p.3509–3521.

DOI: 10.1016/j.patcog.2007.03.017

[3] X.H. Hu, N. Cercone, Learning in relational databases: a rough set approach, Computational Intelligence 11 (1995), p.323–338.

DOI: 10.1111/j.1467-8640.1995.tb00035.x

[4] Z. Pawlak, Rough Sets: Theoretical Aspects of Reasoning About Data, Kluwer Academic Publishers, Boston, (1991).

[5] A. Skowron, C. Rauszer, The discernibility matrices and functions in information systems, in: R. Slowin' ski (Ed. ), Intelligent Decision Support, Handbook of Applications and Advances of the Rough Sets Theory, Kluwer, Dordrecht, (1992).

DOI: 10.1007/978-94-015-7975-9_21

[6] D. Slezak, Approximate reducts in decision tables, Proceedings of Information Processing and Management of Uncertainty (1996), p.1159–1164.

[7] J. Wang, D.Q. Miao, Analysis on attribute reduction strategies of rough set, Chinese Journal of Computer Science and Technology 13 (1998), p.189–192.

DOI: 10.1007/bf02946606

[8] J. Wang, J. Wang, Reduction algorithms based on discernibility matrix: the ordered attributes method, Journal of Computer Science and Technology 16 (2001), p.489–504.

DOI: 10.1007/bf02943234

[9] W.Z. Wu, M. Zhang, H.Z. Li, J.S. Mi, Knowledge reduction in random information systems via Dempster–Shafer theory of evidence, Information Sciences 174 (2005), p.143–164.

DOI: 10.1016/j.ins.2004.09.002

[10] W.X. Zhang, J.S. Mi, W.Z. Wu, Knowledge reduction in inconsistent information systems, Chinese Journal of Computers 1 (2003), p.12–18.

[11] K. Zhao, J. Wang, A reduction algorithm meeting users' requirements, Journal of Computer Science and Technology 17 (2002), p.578–593.

[12] G.Y. Wang, Calculation methods for core attributes of decision table, Chinese Journal of Computers 26 (2003), p.611–615. in Chinese.

[13] M. Yang, Z.H. Sun, Improvement of discernibility matrix and the computation of a core, Journal of Fudan University (Natural Science) 43 (2004), p.865–868. in Chinese.

[14] Y.Y. Yao, Y. Zhao, Discernibility matrix simplification for constructing attribute reducts, Information Sciences 179 (7) (2009), p.867–882.

DOI: 10.1016/j.ins.2008.11.020

[15] D.Y. Ye, Z.J. Chen, An improved discernibility matrix for computing all reducts of an inconsistent decision table, The Proceedings of the Fifth IEEE International Conference on Cognitive Informatics (2006), p.305–308.

DOI: 10.1109/coginf.2006.365511

[16] M. Kryszkiewicz, Comparative study of alternative types of knowledge reduction in inconsistent systems, International Journal of Intelligent Systems 16 (2001), p.105–120.

DOI: 10.1002/1098-111x(200101)16:1<105::aid-int8>3.0.co;2-s

[17] J.S. Mi, W.Z. Wu, W.X. Zhang, Approaches to knowledge reduction based on variable precision rough set model, Information Sciences 159 (2004), p.255–272.

DOI: 10.1016/j.ins.2003.07.004

[18] D. Slezak, Normalized decision functions and measures for inconsistent decision tables analysis, Fundamenta Informaticae 44 (2000), p.291–319.

[19] G.Y. Wang, J. Zhao, J. Wu, A comparitive study of algebra viewpoint and information viewpoint in attribute reduction, Foundamenta Informaticae 68 (2005), p.1–13.

[20] Y. Zhao, Y.Y. Yao, F. Luo, Data analysis based on discernibility and indiscernibility, Information Sciences 177 (2007), p.4959–4976.

DOI: 10.1016/j.ins.2007.06.031

[21] A. Skowron, Boolean reasoning for decision rules generation, Proceedings of the International Symposium on Methodologies for Intelligent Systems (1993), p.295–305.

DOI: 10.1007/3-540-56804-2_28

[22] Y.Y. Yao, Decision-theoretic rough set models, Proceedings of the Second International Conference on Rough Sets and Knowledge Technology LNAI 4481 (2007), p.1–12.

DOI: 10.1007/978-3-540-72458-2_1

[23] T. Beaubouef, F.E. Petry, G. Arora, Information-theoretic measures of uncertainty for rough sets and rough relational databases, Information Sciences 109 (1998), p.185–195.

DOI: 10.1016/s0020-0255(98)00019-x

[24] Q.H. Hu, D.R. Yu, Z.X. Xie, Information-preserving hybrid data reduction based on fuzzy-rough techniques, Pattern Recognition Letters 27 (2006), p.414–423.

DOI: 10.1016/j.patrec.2005.09.004

[25] R. Susmaga, Reducts and constructs in attribute reduction, Fundamenta Informaticae 61 (2) (2004), p.159–181.

[26] I. Düntsch, G. Gediga, Uncertainty measures of rough set prediction, Artificial Intelligence 106 (1998), p.77–107.

DOI: 10.1016/s0004-3702(98)00091-5

[27] J. Klir, M.J. Wierman, Uncertainty Based Information: Elements of Generalized Information Theory, Physica-Verlag, New York (1999).

[28] J.Y. Liang, Z.Z. Shi, The information entropy, rough entropy and knowledge granulation in rough set theory, International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 12 (2004), p.37–46.

DOI: 10.1142/s0218488504002631

[29] M.J. Wierman, Measuring uncertainty in rough set theory, International Journal of General Systems 28 (1999), p.283–297.

DOI: 10.1080/03081079908935239

[30] Y.Y. Yao, Y. Zhao, Attribute reduction in decision-theoretic rough set models, Information Sciences 178 (2008), p.3356–3373.

DOI: 10.1016/j.ins.2008.05.010

[31] Y. Zhao, F. Luo, S.K.M. Wong, Y.Y. Yao, A general definition of an attribute reduct, Proceedings of the Second Rough Sets and Knowledge Technology (2007), p.101–108.

DOI: 10.1007/978-3-540-72458-2_12

[32] D.Q. Miao, J. Zhou, N. Zhang, N. Feng, R.Z. Wang, Research of attribute reduction based on algebraic equations, Acta Electronica Sinica, accepted for publication. (in Chinese).

[33] S.H. Nguyen, H.S. Nguyen, Some efficient algorithms for rough set methods, Proceedings of the International Conference on Information Processing and Management of Uncertainty on Knowledge Based Systems (1996), p.1451–1456.