Construction engineering projects are costly and require large amounts of labor, physical, and financial resources. The failure of a construction engineering project typically brings huge losses. Previous studies have focused on the identification of risks, but insufficient attention has been given to strategic resource allocation for risk management after risk identification. Statistics show that most construction engineering project failures are caused by common risks. Common risks are called gray rhino risks. This metaphor illustrates that many risks are obvious but dangerous. This study was motivated by the challenge of efficiently managing gray rhino risks with limited inputs. The literature suggests that gray rhino risks are abundant in construction engineering projects and that there are mutual eliciting relationships between them, which make it difficult for the manager to devote enough resources to the prevention of key risks. Considerable resources are wasted on unimportant risks, resulting in key risk occurrence and failure of construction engineering projects. Therefore, this study describes an innovative multi-criteria decision making (MCDM) technique for ranking risks based on the strength of the eliciting relationships between them. This study used the fuzzy technique and created an interference fuzzy analytical network process (IF-ANP) method. By employing the IF-ANP alongside a decision-making trial and evaluation laboratory (DEMATEL) approach, the subjectivity can be effectively reduced and the accuracy improved during expert risk evaluation for construction engineering projects. IF-ANP was used to quantify eliciting relationships between risks and DEMATEL was used to rank risks based on the IF-ANP result. An empirical study was done to meticulously rank five risks that were selected from the gray rhino risks in the Chengdu–Chongqing Middle Line High-speed Railway construction engineering project. They are capital chain rupture, decision failure, policy and legal risk, economic downturn, and stakeholder conflict. The results showed that the policy and legal risk was the source of other risks, and that these other risks were symptoms rather than the disease.@en