Reduction Of Ordered Information Table And Reduction Based On Pansystems

Rough set theory considered that knowledge root in classification ability of people or other species. By the research of classification based on difference-identity view in pansystem, we conclude that difference-identity-distinguishing and panorder-ranking are the process of cognition. The concept of pansystem difference-identity is in touch with set theory, and is a systemic concept. Following the "system", we could study the transformation from system to system. And then the research of rough set theory could be done endlessly. Reduction is an important content in rough set theory. The research of reduction in this paper is just based on the difference-identity relation.This paper firstly introduces the difference-identity relation and generalized order relation, analyzes how they are induced respectively, and comes to a conclusion that panorder-ranking is also a kind of difference-identity-distinguishing. Then based on the two relations deeply talks over the essence of reduction of rough set theory. Also this paper gives the reduction concepts of ordered information system based on the importance of ordered problem. And the concepts are the generalization of reduction.Further the reduction algorithm of ordered information system is studied. First the ordered information table and its rule obtaining are introduced. Then an algorithm based on discernibility matrix is presented. An example to prove the algorithm is given following.Finally another algorithm which need not to give discernibility matrix is presented. Without the establishing of discernibility matrix, some space and time are saved.