Reduction algorithms based on discernibility matrix: The ordered attributes method

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.