Research On Multi-Granul Rough Set Under The Dominance Relation And Its Application

With the increase of decision attributes and the emergence of distributed data, it is difficult to find the equivalence class or dominant class of the object under all the attributes.Sometimes the equivalent class or dominant class is only the object itself. At this point, the reduction, classification or ranking method of single-granularity rough sets may be invalid. Multi-granularity rough set can effectively solve this problem and has become a research hot spot. However, the upper and lower approximations of the classical multi-granular rough set are all based on the inclusion relationship and are lacking of ability to adapt to noise data. In this paper, the concept of variable precision and the support function are introduced to the multi-granularity rough set under the dominance relation to improve its tolerance. And the attribute reduction and ranking method of the multi-granularity rough set under the dominance are studied. The main research results are as follows:(1) The concept of variable precision and the support function will be introduced to dominance-based mul-tigranulation rough set. And define a new model of variable multi-granularity rough set under the dominance relation. By introducing two parameters of a and ?, the model is adjusted to enhance the tolerance ability. The disadvantages of the definition about the lower approximation and upper approximation are improved.(2) The lower approximation distribution reduction and the upper approximation distribution reduction of variable multi-granularity rough set are defined. Algorithm steps are given. And the rule extraction method of variable multi-granularity rough set is proposed in this paper. Finally, the effectiveness of the method is verified by the simulation experiment.(3) The shortages of existing sorting method for multi-granularity rough sets under the dominance relation is improved. And a new method based on the relative dominance relation is proposed. The two methods overcome the failure of the original scheduling method when the granularity increases. And the two methods have good mathematical property and good interpretability.