Rough Sets Model Based In Incomplete Information Systems

Classic rough set theory based on equivalence relation takes complete system as object of study , and divides the region into some non-intersect equivalence class. But for some real reasons,there are many information systems which are incomplete. So it is limited in practical application. Therefore, it is crucial to develop rough set theory under incomplete information systems, which is implemented by extending the classical rough set theory.The disadvantages of established models of Missing-value information system, including the model of compatibility relation based rough sets formulated by M. Kryszkiewcz,the model of Asymmetrical similarity relation based rough sets formulated by J. Stefamowski and A. Tsoukeas,the model of limited tolerance relation based rough sets formulated by Guo-Yin Wang and the model ofτlimited tolerance relation based rough sets formulated by Mei-Lian Liang, have been discussed and amend. Then through a concrete instance, the relative merits of four models, when dividing the region into some non-intersect class, are studied in-depth.The fourth chapter has made a study of some more general case, Set-value Information Systems. According to the universality and particularity of Set-value Information Systems, it defines the new function which is used to describe similarity degree of two objects, and the properties are studied. And then, based on the model ofτlimited tolerance relation based rough sets formulated by Mei-Lian Liang, the compatibility relation in Set-value Information Systems is given. The definition shows, two objects has compatibility relation if their attribute value can be the same and the percentage of their similarity degree which is larger thanαi can be higher thanτ. By introducing probability idea, the new successful model is formulated.Next we focused on the correlative characters of the model of Set-value information system based on rough set theory problem. And also we prove its rationality. The new model is the generalization of the established models. Finally, we study the Reduct and algorithm of decision extraction rule.