Reduction Algorithms Based on Discernibility Matrix:The Ordered Attributes Method

In this paper, we present reduction algorithms based on theprinciple of Skowron's discernibility matrix --- the ordered attributesmethod. The completeness of the algorithms for Pawlak reduct and theuniqueness for a given order of the attributes are proved. Since adiscernibility matrix requires the size of the memory of |U|^2, Uis a universe of objects, it would be impossible to apply thesealgorithms directly to a massive object set. In order to solve theproblem, a so-called quasi-discernibility matrix and two reduction algorithms areproposed. Although the proposed algorithms are incomplete for Pawlakreduct, their optimal paradigms ensure the completeness as long as theysatisfy some conditions. Finally, we consider the problem on thereduction of distributive object sets.