关键词: 多粒度决策粗糙集,贝叶斯决策理论,α-下近似分布约简,粒度约简,近似分布质量

Abstract: Multigranulation decision-theoretic rough set method (MG-DTRS) is a generalization of multigranulation rough set model through combining the decision-theoretic rough sets theory and the multigranulation idea,which is a data modeling method on decision-theoretic rough sets in the context of multiple granular spaces.Further,based on Baye-sian decision theory,we made a concrete analysis about probability fusion relations used optimistic or pessimistic fusion strategies on multiple granular spaces,also,the approximate representation of the maximum conditional probability rough sets and the minimum conditional probability rough sets were proposed respectively.And then the optimistic MG-DTRS model and the pessimistic MG-DTRS model were constructed.Furthermore,a concept of the approximate distribution reduction was introduced to MG-DTRS model,and the granular structure selection problem under multiple granular spaces was investigated.Based on the multiple granular approximate distribution quality proposed in this mo-del,the important measure of a granular structure was defined,and an α-lower approximate distribution reduction algorithm to obtain a granular structure reduction was designed under optimistic or pessimistic fusion strategies respectively.Finally,an example was employed for verifying the validity of the proposed algorithm.

Key words: Multigranulation decision-theoretic rough sets,Bayesian decision theory,α-lower approximate distribution reduction,Granular structure reduction,Approximate distribution quality