Fuzzy probabilistic information system (FPIS), a combination of some fuzzy relations on the same universe which satisfies probability distribution, can be regarded as an information system (IS) with fuzzy relations under the probability environment. This means that three types of uncertainty: roughness fuzziness and probability are integrated into an IS. This paper aims to measure the uncertainty of a FPIS. Firstly, information granulation in a FPIS is proposed. Then, information entropy and rough entropy in a FPIS are proposed. Moreover, information amount in a FPIS is also investigated. Finally, the feasibility of the proposed measures are verified by a numerical example, and the statistical analysis is carried out. Those obtained results may be useful for understanding the essence of uncertainty for a FPIS.

模糊概率信息系统(FPIS)是同一宇宙上满足概率分布的一些模糊关系的组合，可以看作是概率环境下具有模糊关系的信息系统(IS)。这意味着三种类型的不确定性：粗糙度模糊性和概率被整合到一个 IS 中。本文旨在测量 FPIS 的不确定性。首先，提出了FPIS中的信息粒度。然后，提出了 FPIS 中的信息熵和粗糙熵。此外，还研究了 FPIS 中的信息量。最后,通过数值算例验证了所提出措施的可行性,并进行了统计分析。这些获得的结果可能有助于理解 FPIS 不确定性的本质。