Research On Some Problems Of Graded Pessimistic Multi-granulation Rough Sets Model

Rough sets theory was put forward by a Polish mathematician Pawlak for the first time in 1982,that is a kind of mathematical theory and that is used for data analysis.Besides,the theory is used as a mathematical tool to deal with imprecise,uncertain and incomplete data.The Pawlak rough sets are based on partition,ignoring the quantized information of the overlapped parts of the class and set,which have a great limitation in the practical application,and the graded rough sets expand the classical rough sets from the absolute quantification of information.In this paper,the variable precision rough sets are combined with the graded rough sets,and we introduce the variable precision graded pessimistic multi-granulation rough sets model.And,we define the lower approximation distribution and the granularity en-troy of the lower approximation distribution.Discussed the important properties and re-lated theorems,further the definition of the reduction and the heuristic algorithm is given,and through the example shows the feasibility of the model.Secondly,four kinds of graded pessimistic multi-granulation rough sets model based on covering are proposed.Based on the evidence theory,the belief structure of the graded pessimistic multi-granulation rough set is given,and the relationship between graded pessimistic multi-granulation rough sets and evidence theory is established.