吴伟志, 杨丽, 谭安辉, 徐优红. 广义不完备多粒度标记决策系统的粒度选择[J]. 计算机研究与发展, 2018, 55(6): 1263-1272.
 引用本文: 吴伟志, 杨丽, 谭安辉, 徐优红. 广义不完备多粒度标记决策系统的粒度选择[J]. 计算机研究与发展, 2018, 55(6): 1263-1272.
Wu Weizhi, Yang Li, Tan Anhui, Xu Youhong. Granularity Selections in Generalized Incomplete Multi-Granular Labeled Decision Systems[J]. Journal of Computer Research and Development, 2018, 55(6): 1263-1272.
 Citation: Wu Weizhi, Yang Li, Tan Anhui, Xu Youhong. Granularity Selections in Generalized Incomplete Multi-Granular Labeled Decision Systems[J]. Journal of Computer Research and Development, 2018, 55(6): 1263-1272.

## Granularity Selections in Generalized Incomplete Multi-Granular Labeled Decision Systems

• 摘要: 粒计算(granular computing, GrC)是知识表示和数据挖掘的一个重要方法,它模拟人类思考模式，以粒为基本计算单位，以建立大规模复杂数据和信息处理的有效计算模型为目标.粒计算主要研究粒的构造、解释、表示、粒度的选择以及用规则形式所描述的粒与粒之间的关系等.针对具有多粒度标记的不完备信息系统的知识获取问题，首先，介绍了广义不完备多粒度标记信息系统的概念，在该信息系统中定义了相似关系，给出了在不同粒度标记层面下信息粒的表示及其相互关系，并定义了基于相似关系的集合的下、上近似概念，给出了近似算子的性质；其次，定义了广义不完备多粒度标记决策系统中的粒度标记选择的概念，阐明了所有粒度标记选择全体构成了一个完备格；最后，讨论了广义不完备多粒度标记决策系统中的最优粒度标记选择问题，并用证据理论中的信任函数和似然函数刻画了协调的不完备多粒度标记决策系统的最优粒度选择特征.

Abstract: Granular computing (GrC), which imitates human being’s thinking, is an approach for knowledge representation and data mining. Its basic computing unit is called granules, and its objective is to establish effective computation models for dealing with large scale complex data and information. The main directions in the study of granular computing are the construction, interpretation, representation of granules, the selection of granularities and relations among granules which are represented by granular IF-THEN rules with granular variables and their relevant granular values. In order to investigate knowledge acquisition in the sense of decision rules in incomplete information systems with multi-granular labels, the concept of generalized incomplete multi-granular labeled information systems is first introduced. Information granules with different labels of granulation as well as their relationships from generalized incomplete multi-granular labeled information systems are then represented. Lower and upper approximations of sets with different levels of granulation are further defined and their properties are presented. The concept of granularity label selections in generalized incomplete multi-granular labeled information systems is also proposed. It is shown that the collection of all granularity label selections forms a complete lattice. Finally, optimal granular label selections in incomplete multi-granular labeled decision tables are also discussed. Belief and plausibility functions in the Dempster-Shafer theory of evidence are employed to characterize optimal granular label selections in consistent incomplete multi-granular labeled decision systems.

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