区间直觉模糊粗糙集的不确定性研究

Research on uncertainty of interval-valued intuitionistic fuzzy rough sets

对区间直觉模糊信息系统中近似集的不确定性进行了研究,给出了区间直觉模糊粗糙集的不确定性度量公式。首先在区间直觉模糊近似空间中,定义了一对具有对称性的新的区间直觉模糊上、下近似算子;其次给出了区间直觉模糊集粗糙隶属函数的定义并讨论了相关性质;最后利用区间直觉模糊粗糙隶属函数的区间直觉模糊熵,定义了区间直觉模糊粗糙集的模糊熵,并讨论了区间直觉模糊粗糙集的模糊熵为零的充要条件,证明了在区间直觉模糊近似空间中经典集合和它的余集的粗糙度量是相等的,以此说明定义的合理性。

The uncertainty of an approximate set in interval-value intuitionistic fuzzy information system is researched in this paper and the uncertainty measurement formula of interval-value intuitionistic fuzzy rough sets are given. Firstly,a pair of new interval-value intuitionistic fuzzy upper and lower approximation operators with symmetry is defined in the interval-value intuitionistic fuzzy approximation space. Secondly,the corresponding definition of rough membership functions on interval-value intuitionistic fuzzy is given and properties are discussed. Finally,the fuzzy entropy of interval-value intuitionistic fuzzy rough set is defined by interval-value intuitionistic fuzzy entropy of the interval-value intuitionistic fuzzy rough membership functions. The necessary and sufficient conditions when the fuzzy entropy on interval intuitice fuzzy rough set is zero are discussed. In addition,the rough measurement values of classic set and residual set are equal in the interval-value intuitionistic fuzzy approximate space,thereby proving the rationality of the definition.