Towards Set Theory-Based Knowledge Reduction

In order to cut down the high cost of knowledge reduction by using discernible matrix (DM), this paper, based on the idea of set operation, 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 forming a set, which can discern a knowledge system. By the formal description for set operation, the related theories of knowledge reduction are constructed, especially the theorem of identity operation in the paper. To illustrate our approach, two cases are analyzed based on these theories. And then two algorithms for knowledge reduction are designed. Algorithm 1 can get all the MDCS of a knowledge system, while algorithm 2 with higher reduction efficiency 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. Knowledge reduction based on set theory involves some new approaches. So, the result of research in this article is only for reference.