多重代价多粒度决策粗糙集模型研究

Multi-Cost Based Multi-Granulation Decision-Theoretic Rough Set Model

决策粗糙集和多粒度粗糙集是两种重要的数据处理机制。在对多重代价决策粗糙集模型和多粒度粗糙集模型的研究基础上,通过综合考虑多重代价矩阵和多粒度思想,将权重均值代价策略引入决策粗糙集模型中,提出了一种基于权重多重代价的多粒度决策粗糙集模型。在不完备信息系统中,分析了悲观代价决策粗糙集、乐观代价决策粗糙集和权重多重代价多粒度决策粗糙集模型,并给出了以上各种模型的决策代价总代价计算公式。以权重多重代价悲观多粒度决策粗糙集模型为例,讨论了该模型下随着粒度的变化其正域的变化情况,并给出了一种基于代价最小化的粒度约简方法。该模型更好地结合了决策粗糙集模型和多粒度粗糙集模型,可从多角度分析解决决策粗糙集模型中的相关问题。

Decision-theoretic rough sets and multi-granulation rough sets are two important mechanisms of data processing.On the basis of decision-theoretic rough sets based on multi-cost and multi-granulation rough sets,by considering multi-cost matrix and multi-granularity thought,this paper introduces a weighted mean-cost strategy into decision-theoretic rough set models,and proposes a multi-granulation decision-theoretic rough set model based on weighted multi-cost.In the incomplete information system,this paper discusses the pessimistic cost decision-theretic rough sets,optimistic cost decision-theoretic rough sets and weighted multi-cost multi-granulation decision-theoretic rough set models respectively,and describes the formulas of the whole decision costs for the above models.Finally,taking the pessimistic multi-granulation decision-theoretic rough set model based on weighted multi-cost for example,this paper analyzes the monotonicity of the decision positive region with respect to knowledge granularity sets,and proposes a definition of the granularity reduction based on the minimum decision cost.The model combines the decision-theoretic rough set model and multi-granulation rough set model with a more suitable method,which can solve the problems from multiple perspectives in the decision-theoretic rough set model.