The Research On Some Problems Of Incomplete Ordered Information And Decision Systems

Rough set theory has been attached importance by domestic and overseas experts and scholars, because it has a great advantage in dealing with uncertain information. This thesis mainly researches incomplete ordered information and decision systems based on rough set theory. Main research tasks are as follows.Firstly, in order to research the uncertainty of the internal structure on incomplete ordered information and decision systems, some information measures are set up, such as knowledge granularity, information entropy, roughness degree, differential quantity of dominance classes and roughness degree of differential quantity of dominance classes. Then complementary nature about knowledge granularity and information entropy is obtained. What’s more, the uncertainty of the internal structure on incomplete ordered information systems can be more accurately measured by the roughness degree of differential quantity of dominance classes. As a result, the importance of attributes in the system is effectively measure, as well as sorting the attributes can be done.Secondly, to research the algorithm of rule extraction in incomplete ordered decision systems, on one hand, the concept of generalized dominance decision function is defined, and the attribute reduction algorithm base on discernibility matrix of generalized dominance decision function is proposed, so that the certain ordered decision rules are extracted. On the other hand, by giving the uncertain dominance matrix, the cores of incomplete ordered information systems is obtained, and then the negative ordered decision rules are extracted. So these rules are used as decision making in incomplete ordered systems.Finally, in order to make up the shortage about tolerance dominance relation and limited dominance relation, α dominance relation is put forward. Base on a dominance relation, the notions of dominance discernibility matrix and dominance decision discernibility matrix are proposed, and then some algorithms of attribute reduction are obtained. Furthermore, in order to improve the efficiency of attribute reduction in incomplete ordered information systems of a dominance relation, a heuristic algorithm is proposed by measuring the attribute significance from the perspective of relative differential quantity of advantage classes.