Study On Some Problems Of Static Rough Sets And Dynamic Rough Sets

Rough sets theory, proposed by Poland mathematician Z. Pawlak in 1982, is a new mathematical tool to deal with vagueness and uncertainty. Keeping the classified ability and using knowledge reduction to get the decision of problem and classified rules is the main idea of rough sets theory. The main advantage of the theory over other techniques is that it does not need any preliminary or additional information about analyzed data. This is the biggest distinction between rough sets theory and other theories dealing with vagueness and uncertainty, such as probability theory, fuzzy theory, evidence theory. Now, rough sets theory has extensive applications in data mining, pattern recognition, decision analysis and so on.The thesis consists of five chapters and studies some important problems of stamic rough sets (Z. Pawlak rough sets) and dynamic rough sets (S-rough sets). The problems include rough communication of classical concepts, rough communication of fuzzy concepts, and some characteristics of assistant set on S-rough sets. etc.Chapter one provides the basic concepts and structure of rough sets and S-rough sets.Chapter two discusses some problems of rough communication of classical concept. The main results are as follows:Theorem 1 Let (U,R₁), (U,R₂),……, (U,R_n) be n approximation spaces, which represent the knowledge of agent 1, agent 2, ……, agent n respectively (n≥2). Given a crisp concept X (?)U, in the n ! translation sequence, all the translation results of rough communication are There must be...