Abstract: 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.

Key words: decision-theoretic rough set, multi-granulation rough set, decision cost, reliability of cost

摘要： 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。

关键词: 决策粗糙集, 多粒度粗糙集, 决策代价, 代价认可度