针对传统多粒度粗糙集模型在反映问题的不完全性与统计特性方面的局限性,提出了多粒度概率粗糙集模型。首先,将概率粗糙集模型的思想与粒计算中多粒度空间描述问题的思想相结合,给出具有一般性的多粒度概率粗糙集模型的定义。同时,以正域及负域不变的原则定义了乐观多粒度概率粗糙集模型的属性约简。然后,基于Bayes最小风险理论对多粒度概率粗糙集模型中的参数进行确定。最后,将乐观多粒度概率粗糙集模型应用于弹道导弹目标识别问题中。

In order to eliminate incompleteness and limitation in statistics of multi-granulation rough set, a multi-granulation rough set model was proposed by probabilistic rough set theory. First, probabilistic rough set theory was combined with multi-granulation theory and came up with the generalized definition about multi-granulation probabilistic rough set model. Abiding by the rules that positive region and negative region keep invariable, the attribute reduction for the optimistic model was defined. Then based on minimum Bayes expected risk decision theory, two parameters of multi-granulation probabilistic rough sets model were computed. Finally, the optimistic multi-granulation probabilistic rough sets model was applied to a case study of target recognition.