Study On Multi-granulation Decision-theoretic Rough Sets Models

Multi-granulation decision-theoretic rough sets are effective tools to deal with un-certain problems,which have been widely used in many decision problems.Taking the multi-granulation decision-theoretic rough sets as the research object,this paper sys-tematically and deeply studies the models in interval-valued information system and the models combined with hesitant fuzzy set.In interval-valued information system,firstly,we utilize the basic set assignment function to deal with tolerance classes to construct the probability measure spaces,and establish the decision-theoretic rough sets in interval-valued information system.Second-ly,combined with multi-granulation rough sets,the multi-granulation decision-theoretic rough sets are constructed.When the scale of data set is large,it takes a lot of time to characterize the approximations of the target concept,and the calculation processes is also very complex.In order to overcome this limitation,we further establish the local multi-granulation decision-theoretic rough sets models in interval-valued information sys-tem,that is,optimistic and pessimistic local multi-granulation decision-theoretic rough sets models,and study their properties,establish three-way decisions models.And then compare this model with the multi-granulation decision-theoretic rough sets models by combining with an example.At the same time,an algorithm is designed to verify the fea-sibility and simplicity of the method.This method is very useful for rough data analysis on large scale data sets.Hesitant fuzzy set is an extension of fuzzy set.Combining hesitant fuzzy set with decision-theoretic rough sets,the hesitant fuzzy decision-theoretic rough sets models are constructed on the basis of the inclusion degree of hesitant fuzzy set.And then fur-ther combining with multi-granulation rough sets,the optimistic and pessimistic multi-granulation hesitant fuzzy decision-theoretic rough sets models are established,and their properties are studied.Then,the corresponding three-way decisions models are given.Finally,an example is given.