Reduction algorithms based on discernibility matrix: The ordered attributes method. (English) Zbl 1014.68160

Summary: We present reduction algorithms based on the principle of Skowron’s discernibility matrix – the ordered attributes method. The completeness of the algorithms for Pawlak reduct and the uniqueness for a given order of the attributes are proved. Since a discernibility matrix requires the size of the memory of \(|U|^2\), \(U\) is a universe of objects, it would be impossible to apply these algorithms directly to a massive object set. In order to solve the problem, a so-called quasi-discernibility matrix and two reduction algorithms are proposed. Although the proposed algorithms are incomplete for Pawlak reduct, their optimal paradigms ensure the completeness as long as they satisfy some conditions. Finally, we consider the problem on the reduction of distributive object sets.


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[1] Pawlak Z. Rough Set – Theoretical Aspects of Reasoning about Data. Kluwer Academic Publishers, Dorderecht, Boston, London, 1991. · Zbl 0758.68054
[2] Skowron A, Rauszer C. The Discernibility Matrices and Functions in Information Systems. Intelligent Decision Support – Handbook of Applications and Advances of the Rough Sets Theory, Slowinski R (ed.), 1991, pp.331–362.
[3] Wang J, Miao D. Analysis on attribute reduct strategies of rough set.Journal of Computer Science and Technology, 1998, 13(2): 189–193. · Zbl 0902.68049
[4] Wang J, Wang R, Miao Det al. Data enriching based on rough set theory.Chinese Journal of Computers, 1998, 21(5): 393–400.
[5] Wang J. Rough Sets and Their Applications in Data Mining. Fuzzy Logic and Soft Computing, Chen G (ed.), Kluwer Academic Pub., 1999, pp.195–212.
[6] Quilan J. Induction of Decision Trees. Machine Learning 1, 1986, pp.81–106.
[7] Utgoff P. ID5: An Incremental ID3. InProceeding of ICML-88, Ann Arbor, MI: Morgan Kaufmann 1988, pp.107–120.
[8] Polkowski L, Skowron A. Rough Sets: Perspectives. Rough Sets in Knowledge Discovery 1, Polkowski L, Skowron A (eds.), Physica-Verlag, 1998, pp.1–27. · Zbl 0910.00028
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