多粒度决策粗糙集中的粒度约简方法

Granular Structure Reduction Approach to Multigranulation Decision-theoretic Rough Sets

多粒度决策粗糙集模型是一种泛化的多粒度粗糙集模型,该模型结合决策粗糙集数据分析理论和多粒度思想,实现了在多个粒空间进行决策粗糙集理论的建模。在此基础上,利用贝叶斯决策理论具体分析了在多粒度粗糙集模型中乐观和悲观的融合策略下多个粒空间中的概率融合关系,推导出基于最大条件概率和最小条件概率的粗糙集近似表示,进而构建了乐观多粒度决策粗糙集模型和悲观多粒度决策粗糙集模型。在该模型中引入近似分布约简的概念,分析了多个粒空间中的粒度选择问题。基于多粒度近似分布质量定义了多粒度决策粗糙集的粒度重要度,并且基于此给出了悲观和乐观融合策略α-下近似分布约简的粒度约简算法。通过实例验证了该算法的有效性。

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 da- ta 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 probabilityrough 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 distri- bution reduction was introduced to MG-DTRS model, and the granular structure selection problem under multiple gran- ular 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 a-lower approximate distribution reduction algo- rithm to obtain a granular structure reduction was designed under optimistic or pessimistic fusion strategies respective- ly. Finally,an example was employed for verifying the validity of the proposed algorithm.