Research On The Neighborhood Multi-granulation Rough Set Model And Algorithm Oriented Mixed Data

Rough set theory,a mathematic tool, which can deal with imprecision and uncertain information effectively, was proposed by Poland scholar Z.Pawlak in 1982.Classical rough set theory only can deal with categorical attributes, can not handle numerical attributes and the heterogeneous data including categorical attributes and numerical attributes. In order to solve this problem, by means of neighborhood relationships instead of equivalence relation, Lin put forward a neighborhood rough set model. From the point of view of granular computing, the rough set above is based on single-granularity and sheer-level, and can not analyze and process the problems from the multi-granularity and multi-level. Yuhua Qian and jiye liang etc put forward a sort of optimistic and pessimistic multi-granularity rough set model, 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-granularity theory domain space. Optimistic multi-granularity rough set model is relatively loose, and pessimistic multi-granularity rough set model is relatively strict, therefore, Zhang Ming put forward a kind of Variable granulation rough set model to overcome the above disadvantages. Combining with the advantages of multi-granularity rough set model and neighborhood rough set model, extending the neighborhood rough set model to multi-granularity space, Guoping Lin put forward a concept of Neighborhood Multi-granularition rough set model, with different combinations of categorical attributes and numerical attributes to build property set sequence, as a granulate criterion, defines two Neighborhood Multi-granularity rough set models. However, the model was established on the same radius of neighborhood, therefore, it can only handle the problem of fixed neighborhood radius. According to the above, this paper has obtained the following results:(1) By analyzing the weakness of traditional rough set and neighborhood multi-granularity rough set, overcoming the shortcoming of relatively loose optimistic multi-granularity rough set model and more stringent pessimistic multi-granularity rough set model, dealing with the heterogeneous data including categorical attributes and numerical attributes from the multi-granularity and multi-level perspective, and combining with the neighborhood multi-granularity rough set and Variable Granulation rough set model, Variable Granulation Neighborhood rough set model is proposed in this paper. Furthermore, the formal definition of the upper and lower approximation sets of Variable Granulation Neighborhood rough set model were given, and that Variable granulation Neighborhood rough set is the generalization of optimistic multi-granularity rough set model and pessimistic multi-granularity rough set model was proved, and the properties of this rough sets model was discussed.(2) In order to deal with the heterogeneous data including categorical attributes and numerical attributes from the multi-granularity and multi-level perspective effectively, double granulate criterion is built on different attribute sets sequence and different neighborhood radii. Neighborhood multi-granulation rough set model based on double granulate criterion is proposed. Several relevant properties of the model are given. An attribute reduction algorithm of the new model is presented. The reduction result can choose the appropriate attribute set and neighborhood radius flexibly according to the need of practical problems. The effectiveness of the proposed model and algorithm is verified by some examples. Therefore, an attribute reduction algorithm of neighborhood multi-granulation rough set model based on double granulate criterion is proposed. Using this algorithm, we can get the reduction sets of the granularity set in the premise of that it do not change the lower approximation distribution of the decision making.