Attribute Reduction Approach To An Ordered Information System Based On Boolean Matrix

Ordered information system is a kind of information system which is based on ordered relation. With the increasing amount of data, how to use effective methods to find the useful information and make it valid is very necessary. Therefore, attribute reduction plays an important role in the studies of ordered information system. Existing mathematical software can calculate matrixes with higher efficiency and smaller storage space in shorter time. So it is meaningful to study the theorems of ordered information system by Boolean matrix method, which is simpler and more practical.In this thesis, the attribute reduction of ordered information system is studied. Based on Boolean Matrix, we mainly study the attribute reduction of ordered information and the attribute reduction of consistent ordered decision information system.The content can be summarized as follows:1. For an ordered information system, defined by Boolean matrix, the coordinated set and attribute reduction based on dominance relation are proposed. Furthermore, the approach to attribute reduction and the judgment theorem of the core attribute are presented. And then, we design an attribute reduction algorithm and prove the effectiveness of the algorithm with practical examples. Finally, the relation between the attribute reduction based on Boolean Matrix and the attribute reduction based on discernibility matrix of ordered information system is obtained.2. First, we represent ordered decision information system by Boolean matrix, and then, for a consistent decision ordered information system, the coordinated set and attribute reduction based on dominance relation are proposed. Furthermore, the approach to attribute reduction and the judgment theorem of the core attribute of consistent ordered decision information system are presented. Then we design an attribute reduction algorithm and prove the effectiveness of the algorithm with practical examples. Finally, the relation between the attribute reduction based on Boolean Matrix and the attribute reduction based on discernibility matrix of consistent decision ordered information system is obtained.