在不完备信息系统中上、下近似的模糊化

Fuzzed of Lower and Upper Approximation in Incomplete Information System

在不完备信息系统中,对象存在不确定性。基于对象的不确定性,讨论一种不完备信息系统中上、下近似的模糊化,即,上、下近似是论域上的一对模糊集合。一方面,在不完备信息系统中,集合的上、下近似由相似关系确定;另一方面,由于"*"的存在,使得对象具有不确定性。因此,首先定义了对象的不确定性程度和对象之间的相似度;然后利用对象之间的相似度,通过逻辑关系和相应的函数运算,分别给出了对象隶属于上、下近似集合的隶属度,形式地,该过程可理解为上、下近似集合的模糊化。实例分析说明在不完备信息系统中,考察对象对于上、下近似的隶属度能更直观、合理地反应对象隶属于某一集合的上、下近似的情况。

The uncertainty of objects is considered in the incomplete information system. Based on the uncertainty of objects,the method in which lower and upper approximation are fuzzed,i. e.,the lower and upper approximation is a pair of fuzzy sets, was discussed in the incomplete information system. Onc hand, lower and upper approximations arc decided by the similarity relation;on the other hand,the objects with uncertainty due to“＊”is existent Therefore, the uncertainty degree of an object and similarity degree among the objects were defined. Then the membership degree of the object belonging to lower and upper approximation was given by similarity degree. Formally,the process is considered as fuzzed of the lower and upper approximation sets. Finally, an example shows that membership degrees more visualy and reasonably describe that objects belong to the lower and upper approximation of the set.