A fuzzy probability approximation space (FPA-space) is a approximation space (A-space) where three types of uncertainty (probability, fuzziness and roughness) are combined, which is obtained by putting probability distribution into a fuzzy approximation space (FA-space). This paper studies relationships between FPA-spaces and and their entropy measurement. Two types of fuzzy relation matrices are first defined by introducing the probability into a given fuzzy relation matrix in two ways, and on this basis, they are extended to two FA-spaces. Then, equality, dependence and independence between FPA-spaces are studied. Next, the distance between FPA-spaces is discussed. Moreover, the uncertainty for an FPA-space is measured by means of information entropy. Finally, the proposed information entropy is applied in the selection of classifier systems. Since fuzzy set theory, probability theory and rough set theory are aggregated together in an FPA-space, the obtained results of this paper may be helpful for dealing with practice problems with a sort of uncertainty.

模糊概率近似空间（FPA -space）是一种近似空间（甲-space）其中三种类型的不确定性（概率，模糊性和粗糙度）相结合，这是通过将概率分布为一个模糊近似空间而获得（FA -space ）。本文研究了FPA空间及其熵测量之间的关系。首先通过两种方式将概率引入给定的模糊关系矩阵来定义两类模糊关系矩阵，并在此基础上将它们扩展到两个FA-空间。然后，平等之间的依赖与独立FPA -spaces进行了研究。接下来，FPA之间的距离-spaces 进行了讨论。此外，FPA空间的不确定性是通过信息熵来测量的。最后，将所提出的信息熵应用于分类器系统的选择。由于模糊集理论、概率论和粗糙集理论在一个FPA空间中聚合在一起，本文得到的结果可能有助于处理具有某种不确定性的实践问题。