Reduction Algorithms Based on Discernibility Matrix：The Ordered Atributes 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 bojects,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 prpopsed.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.

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. This work is supported by the National Key Project for Basic Research on Image, Speech, Natural Language Understanding and Knowledge Mining (NKBRSF, No. G1998030508), the National ‘863’ High-Tech Programme and the National Natural Science Foundation of China. WANG Jue is a professor of computer science and artificial intelligence at Institute of Automation, The Chinese Academy of Sciences. His research interests include artificial intelligence, artificial neural network, machine learning and knowledge discovery in databases. WANG Ju is a professor of computer science at Institute of Software, The Chinese Academy of Sciences. His research interests include logic and its applications in artificial intelligence and computer science.