Fuzzy approximation spaces (FA-spaces) can be seen as approximation spaces (A-spaces) in a fuzzy environment. This article studies relationships between FA-spaces and their uncertainty measures. Dependence, partial dependence and independence between FA-spaces, as characterized by the inclusion degree, are first proposed. Then, the distance between FA-spaces is considered in terms of the angle of difference. Next, algebraic, map and lattice features of FA-spaces are obtained. Finally, the uncertainty of FA-spaces is measured by using the dependence between them, an application is given, and to assess the performance of the presented measures, two examples are used to perform effectiveness analysis by means of elementary statistical methods.

模糊近似空间（FA空间）可以看作是模糊环境中的近似空间（A空间）。本文研究FA空间及其不确定性度量之间的关系。首先提出了以包含度为特征的FA空间之间的依赖性，局部依赖性和独立性。然后，根据差角考虑FA空间之间的距离。接下来，获得FA空间的代数，映射和晶格特征。最后，FA的不确定性通过使用空间之间的依赖关系来度量空间，给出了一个应用程序，并且为了评估所提出的度量的性能，使用两个示例通过基本统计方法进行有效性分析。