The Research On Some Problems Of A Multi—Granulation Probabilistic Rough Set

The advantage of rough set theory is that rough set can analyze data and process data objectively without any prior information. But dealing with the inconsistent system, classical rough set exists deficiencies when dealing with the inconsistent information, because some random information and incomplete information are ignored. Multi-granulation rough sets provide a way to solve the problem. Multi-granulation rough sets and rough set are based on indiscernibility relation with containment relation. Nonetheless, in real-world application, data set does not make equivalence partitioning because of being affected by a noisy data. Data set is lack of ability to adapt to a noisy data, and cannot cope with inclusion relation and part of the relation. In view of these shortcomings, multi-granulation rough set models are based on probability distribution theory from the following aspects to research this paper.Firstly, new multi-granulation rough set models are presented, called multi-granulation probabilistic rough set models. Multi-granulation probabilistic rough sets not only enhance the ability of coping with data, but also overcome the insufficiencies of the too strict lower approximation and the too loose upper approximation of multi-granulation rough sets. Multi-granulation rough sets are extended to be multi-granulation probabilistic rough sets. Properties of multi-granulation probabilistic rough sets are investigated. And the new models are applied to location problem of supermarket.Secondly, granularity reduction methods of multi-granulation probabilistic rough set models and the rule extraction are presented. In the multi-granulation spaces, it is difficult to cope with the greater data of the incontinent information system, because of existing redundant granularities. It is an extremely crucial content to research the rule extraction of multi-granulation probabilistic rough sets. This paper, through distribution function to make the rule extraction, deletes redundant granularities to find granularities reduction of optimistic multi-granulation probabilistic rough set. And this theory is applied successfully to evaluation about commercial risk investment.Thirdly, a variable multi-granulation probabilistic rough set is established, combining multi-granulation rough set with variable multi-granulation rough set. The variable multi-granulation rough set is based on the complete information, adjusting the particle size number to get a lower approximation, which is between a lower approximation of optimistic multi-granulation rough set and a lower approximation of pessimistic multi-granulation rough set. In a real-world application, owing to be affected by the noisy data, it is insufficient to use the theory to dispose of the problem of inclusion relation to some extent. Hence, according to imply the probability theory to variable multi-granulation rough set, author establishes a variable multi-granulation probabilistic rough set model. And its properties are investigated. This model can deal with the database with noisy data and inclusion degree.