Research On The Multi-Granulation Rough Set Models In Incomplete Fuzzy Order Information Systems

Rough set theory was put forward in1980s, which has provided the new technology for information processing. With the rapid development of granular computing, combing the rough set theory with granular computing is a new direction of rough set theory. Qian introduces the rough set into granular space and establishes multi-granulation rough set model based on equivalence relation in complete information systems. The model is a rough data modeling method based on multi-granular space. This thesis mainly researches on the models of muti-granulation rough set in incomplete fuzzy order information systems. The main work is as follows:Firstly, since some data exited in real life is uncertain and fuzzy, in order to solve these problems, the models of multi-granulation rough set in incomplete fuzzy order information systems are established, which is based on the existed rough set models in incomplete fuzzy order information systems. Then the optimistic multi-granulation rough set model and pessimistic multi-granulation rough set model are presented respectively. And some properties and conclusion are presented. At the same time, to solve the problem of uncertain measurement of muti-granulation rough set, a concept of approximation accuracy is defined. And the relationship of approximation accuracy is discussed between single granulation rough set and muti-granulation rough set.Secondly, the proposed optimistic multi-granulation rough set model is deeply discussed. Considering the complexity and redundancy of data in real life, in order to get more effective information, a method to get the attribute reduction is presented. It is the method that is using the relative discernibility function to get the relative lower and upper approximation of multi-granulation rough set via the Boolean reasoning. After getting the attribute reduction, then the decision rules of multi-granulation rough set are also got. At the end, in order to have a non-redundant granular space, an algorithm of granular space reduction based on granular importancy is designed.Thirdly, to solve problems such as the attribute values are interval fuzzy values, the methods of multi-granulation rough set in incomplete fuzzy order information systems are introduced to the interval-valued fuzzy information systems. Then the models of optimistic multi-granulation rough set model and pessimistic multi-granulation rough in interval-valued fuzzy information systems are established.