Research On Some Problems Of Multi-granularity Rough Soft Set

The era of data explosion has arrived owing to the exponential growth of data.Facing with the growing number of data,everyone cannot emphasize the importance of extracting effective information from redundant data quickly and efficiently too much.Some of these data are uncertain,but rough set theory and soft set theory provide us with solutions.But there are still limitations in data processing with noise.Therefore,how to build an effective mathematical model to make favorable decision is important from the point of weight and probability.This paper bases on conditional probability,rough sets,soft sets and the idea of multi-granularity which produces mixed models-weighted multi-granularity rough soft set model and optimistic(pessimistic)multi-granularity probability rough set model.The weighted multi-granularity rough soft set model has the advantage that is the effect of granularity varies in granularity space,resulting in different weights.It can provide decision makers with a more comprehensive and reliable decision.There is no doubt that multi-granularity probability rough soft sets can make full use of the incompleteness and probability characteristics of information.The advantage of the new model is that it keeps the original information space perfectly and greatly improves the ability to process redundant information.Firstly,this paper analyzes the research status of rough sets and soft sets.Moreover,we find the vacancy of the research.Secondly,this paper mainly introduces the related theoretical knowledge of rough sets,soft sets and rough soft sets,which provides research ideas for the proposed new model.Thirdly,this paper presents weighted multi-granularity rough soft set model and optimistic(pessimistic)multi-granularity probability rough set model.Then,we give the basic properties and theorems of these new models and proof them.Finally,some algorithms are proposed for decision-making problems.For example,problem of company application and alternative selection of chemical materials.The simple example shows us the effectiveness of these new algorithms.