Abstract:

Granular computing is a problem processing paradigm based on multi-level structure, which has attracted extensive attention of domestic and foreign scholars in recent years. Granular transformation and problem solving are key issues of multi-granular computing. However, the algebraic quotient space model lacks discussion of these issues. In light of above problems, for the algebraic quotient space model, three complete clusters of algebraic quotient space are defined according to the algebraic quotient space construction methods, so as to analyze and demonstrate the closeness of granular conversion. Furthermore, for different granularity principles and modes, the complete algebraic granularity conversion methods are given from multiple angles. Next, the similarities and differences between different conversion methods and the relationship between granularity conversion results of the algebraic are discussed. In addition, in order to describe the solution results of algebraic problems after coarse grain and fine grain transformations, the consistency principle of solution results is proposed based on the granularity transformation method and algebraic solution rules. The reliability of the granularity conversion methods and the consistency principle is proven by theoretical analysis, and the effectiveness of the proposed methods is verified by an example. The example results are consistent with the theoretical analysis conclusions, which proves the correctness of the consistency principle. It solves the core problem of granular computing using algebraic quotient space model, and provides a theoretical basis for solving large-scale complex problems using algebraic granular computing.

Key words: granular computing, algebraic quotient space, multi-granularity, granularity conversion, consistency

摘要：

粒度计算是一种基于多层次结构的问题处理范式，近年来受到国内外学者的广泛关注。粒度转换技术与问题求解是进行多粒度计算的关键，然而代数商空间却缺乏对这两个重要问题的讨论。为此，针对代数商空间模型，首先，根据商空间的构造方法定义三种完备的代数商空间簇，以论证代数粒度转换的封闭性。在上述工作基础上，针对不同的粒化准则与粒化方式，从多角度给出完整的代数粒度转换方法，并详细讨论了不同转换方法的异同以及粒度转换结果之间的关系。其次，为描述代数问题在粗细粒度转换中的求解结果，基于粒度转换方法与代数求解规则，提出求解一致性原理。通过理论分析证明了粒度转换方法与一致性原理的可靠性，以实例验证了所提方法的有效性，且实例结果与理论分析结论相符合，佐证了一致性原理的正确性；解决了使用代数商空间模型进行粒度计算的核心问题，为使用代数粒度计算求解大规模复杂问题提供了理论依据。

关键词: 粒度计算, 代数商空间, 多粒度, 粒度转换, 一致性