A New Approach to Knowledge Reduction Based on the Set Theory

As a practical method for knowledge reduction, discernible matrix (DM) has been widely used in practice. However, due to the high cost of constructing and reducing of a matrix, the efficiency of this method falls far short of people´s demands. In order to decrease the cost of knowledge reduction based on the ideas of set theory, the paper presents a new approach, which is called the minimum discernible core set (MDCS). Beginning at the selection of an indiscernible attribute, other attributes are added one by one until obtaining a set, which can discern a knowledge system. The paper focuses on the related theories and algorithms of knowledge reduction. Algorithm 1 can get all the MDCS of a knowledge system, while Algorithm 2 that has lower time can get a MDCS of that by using heuristic search rules. Compared with time complexity and space complexity of DM, MDCS has less time and space according to our analysis for the algorithms of DM and MDCS.