Extended Models Research Based On Multi-granulation Rough Set Model

Poland scholar Z. Pawlak proposed the rough set theory in 1982, which has been widely used in many fields. Based on the analysis of the data sets, this theory can solve the practical problems without a priori knowledge. But this theory is based on strict inclusion relation, so the theory can not be applied to noise data. Meanwhile, the traditional rough set theories do the classification of domain based on a single equivalence relation. From the perspective of granular computing, the single-size and single-level features make the traditional theories lack of multi-angle when they are processing on information. To solve the problems, Ziarko introduces variable precision concept in rough set theory, which makes rough set theory has fault tolerant ability and lay a theoretical foundation for obtaining approximate decision rule; Yuhua Qian and Jiye Liang etc. put forward multi-granulation rough set models, which can construct multi-granularity theory domain space by dividing a few indiscernibility relation and multiple domain level, and then approximate to target concept on the multi-granulation theory domain space. Though this way they make rough set theory has the ability of processing information from multi-angle, and further promote the development of rough set theory. Variable precision multi-granulation rough set development based on variable precision rough set model and multi-granulation rough set model, this theory combines their advantages, enhances the ability of processing incomplete information, and the modle can approximate concept from perspective of multi-granulation; On the other hand, Ming Zhang put forward multi-granulation rough set based on weighted granulations on the basis of multi-granulation rough set. The model considers both the quality and quantity of knowledge granularity. So that, this model has more comprehensive study on knowledge granularity, can adapt to the multi-granulation rough set model’s application environment much more better. But the two improved models also have their own shortcomings, on the basis of the above models, achieved the following results:Traditional variable precision multi-granulation rough sets are based on a single threshold, while the multi-granulation rough set model is from multiple perspectives and multi-level processing data. The data acquisition methods of different knowledge granularity is not the same and the noise data is also different. So the variable precision threshold of different knowledge granularity level should be different, which makes the traditional model can not adapt to the multi-granulation environment. In order to solve this problem, a variable precision multi-granulation rough set based on multiple threshold has been proposed. The model makes the variable precision threshold of different levels of knowledge granularity can be adjusted independently, and it is more consistent with the data features of the multi-granulation rough set model. The model combines the multi-granulation rough set and the variable precision rough set model with a more suitable method, which can solve the problem from multiple perspectives and also has more flexible fault tolerance ability.Multi-granulation rough set model based on weighted granulations only considers the simple summation of weighted granulations, without considering the weight distribution, which is not in conformity with the practical problems. After analyzing above problems, from the perspective of weight distribution, multi-granulation rough set model based on weight distribution is proposed. Two common forms of multi-granulation rough set model based on weight distribution are defined, they are multi-granulation rough set model based on weighted combination distribution and multi-granulation rough set model based on weighted average distribution. Some properties are given and the effectiveness of the proposed model is verified by example and simulation experiment.