二元论域知识粒的分解性研究

Research on Decomposition of Knowledge Granules in Binary Domain

粒计算是人类抽象和表达知识的形式化方法,粒度结构抽象与转换是进行多粒度计算的关键,通过分解与合成策略可将复杂问题粒与简单问题粒进行映射和聚合,从而得到解决复杂问题的有效方法.文章针对不同数据环境下笛卡儿积论域上知识粒分解与合成进行了深入研究.首先,对二元论域上精确集、模糊集、直觉模糊集的分解性进行了探讨,分别给出了其可分解的判别条件并证明了其充要性;其次,根据其判别条件分别得到了精确知识粒和粗糙知识粒、模糊知识粒和模糊粗糙知识粒、直觉模糊知识粒和直觉模糊粗糙知识粒可分解条件,进一步揭示了不同知识粒分解的客观规律;最后,依次提出了二元论域上精确集、模糊集、直觉模糊集可分解性判定算法。二元知识粒度分解研究对于完善信息粒度计算理论和降低高维数据计算问题具有重要意义。

Granular computing is a formal method to abstract and express knowledge,and the abstractiont and trans-formation of granular structure is the key to multi-granular computing.Through decomposition and synthesis strate-gy,complex problem particles and simple problem particles can be mapped and aggregated,so as to obtain an effective method to solve complex problems.The decomposition and synthesis of knowledge particles in Cartesian product do-main under different data environments are studied in this paper.Firstly,the factorability of exact sets,fuzzy sets and intuitionistic fuzzy sets in binary discourse universe is discussed,and the discriminant conditions for their factorability are given and their essential properties are proved.Secondly,according to the discriminant conditions,the factorable conditions of exact knowledge grains and rough knowledge grains,fuzzy knowledge grains and fuzzy rough knowledge grains,intuitionistic fuzzy knowledge grains and intuitionistic fuzzy rough knowledge grains are obtained respectively,which further reveals the objective law of decomposition of different knowledge grains.Finally,algorithms for determining the decomposability of exact sets,fuzzy sets and intuitionistic fuzzy sets in binary discourse universe are proposed.The study of binary knowledge granularity factorability is of great significance for perfecting the theory of information granularity calculation and reducing the problem of high-dimensional data calculation.