Failure mode and effect analysis (FMEA) has been widely applied as a powerful reliability analysis technique to identify and eliminate system failures in various industries. Though many contributions have been made to improve the traditional FMEA, some challenges still exist. For example, how to deal with different types of risk information involved in FMEA due to the heterogeneity of risk factors. Additionally, the influence of the relationship between failure modes and the attenuation effect on the final risk priority deserves further study. Motivated by these challenges, we propose an improved risk prioritization method. First, heterogeneous information expression structures (i.e., crisp numbers, interval numbers, triangular fuzzy numbers, linguistic Z-numbers) are utilized to describe risk factors from quantitative and qualitative aspects. Then, the initial risk priority numbers (RPNs) of failure modes are determined without transforming different representation structures into a unified one. Next, the total relation influence matrix is generated considering attenuation effects. Afterward, the PageRank algorithm is extended to obtain the final risk priority by analyzing the mutual influence between failure modes and their initial RPNs simultaneously. Finally, a case study of FMEA for a shipboard medium voltage DC power system is presented to verify the effectiveness of the proposed method. The results indicate that our method can process the heterogeneous risk information more flexibly and prioritize the failure modes more reasonably.