积模糊粗集模型及其模糊知识粒的表示和分解

Representation and Decomposition of Fuzzy Knowledge Granularity Based on Product Fuzzy Rough Set Model

为处理人工智能中不精确和不确定的数据和知识,Pawlak提出了粗集理论。之后粗集理论被推广,其方法主要有二:一是减弱对等价关系的依赖;二是把研究问题的论域从一个拓展到多个。结合这两种思想,研究基于两个模糊近似空间的积模糊粗集模型及其模糊粗糙集的表示和分解。根据这种思想,可以从论域分解的角度探索降低高维模糊粗糙集计算的复杂度问题。先对模糊近似空间的分层递阶结构———λ-截近似空间进行研究,得到不同层次知识粒的相互关系;然后定义模糊等价关系的积,并研究其性质及算法;最后构建基于积模糊等价关系的积模糊粗集模型,并讨论了该模型中模糊粗糙集的表示及分解问题,分别从λ-截近似空间和一维模糊近似空间的角度去处理,给出了可分解集的上(下)近似的一个刻画,及模糊可分解集的上(下)近似的λ-截集分解算法。

Pawlak proposed the rough set theory in order to process data and knowledge which are imprecise or uncertainty in artificial intelligence.And then,the theory got extended.There’re generally two methods：one is to weaken the dependence on equivalence relations,the other is to develop domains to be studied from one to many.Based on the two kinds of thoughts,we researched a product fuzzy rough set model based on two fuzzy approximate spaces,and representation and decomposition of fuzzy rough sets in the product fuzzy approximation spaces.We could explore questions of fuzzy knowledge Granularity’s expression from different angles in the high dimension fuzzy knowledge space.We first researched hierarchical structure of a fuzzy approximation space——λ-cut approximation spaces,and gained the relationship between vary hierarchical knowledge granularity.Secondly,the product of finite fuzzy equivalence relations was defined,and its algorithm was investigated.Finally,a product fuzzy approximation space was constructed based on pro-duct fuzzy equivalence relations,and decompositions of upper and lower approximations of fuzzy sets were discussed in the high dimension fuzzy approximation space,and a characterization of upper（lower） approximation of crisp decomposable sets was given.