Reduction algorithms based on discernibility matrix: The ordered attributes method
- 209 Downloads
In this paper, 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.
Keywordsrough set theory principle of discernibility matrix inductive machine learning
Unable to display preview. Download preview PDF.
- Pawlak Z. Rough Set — Theoretical Aspects of Reasoning about Data. Kluwer Academic Publishers, Dorderecht, Boston, London, 1991.Google Scholar
- 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.Google Scholar
- Wang J, Wang R, Miao Det al. Data enriching based on rough set theory.Chinese Journal of Computers, 1998, 21(5): 393–400.Google Scholar
- 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.Google Scholar
- Quilan J. Induction of Decision Trees. Machine Learning 1, 1986, pp.81–106.Google Scholar
- Utgoff P. ID5: An Incremental ID3. InProceeding of ICML-88, Ann Arbor, MI: Morgan Kaufmann 1988, pp.107–120.Google Scholar
- Polkowski L, Skowron A. Rough Sets: Perspectives. Rough Sets in Knowledge Discovery 1, Polkowski L, Skowron A (eds.), Physica-Verlag, 1998, pp.1–27.Google Scholar