Recently, the melting of Arctic sea ice and development of maritime technology are enabling the regular voyages in Arctic waters. However, the Arctic maritime transportation system (AMTS) is a complex and dynamic system with respect to human, technical, environmental and organizational issues. For example, ships operating in Arctic waters suffer severe weather conditions, fully and partially ice-covered waters, and are also difficult to search and rescue in ice-covered Arctic waters due to remoteness from lands. These risk factors will influence the safety and security of ships operating in Arctic waters. For this, this paper identifies potential risk influencing factors (RIFs) for the AMTS from human, technical (ship), environmental and organizational aspects. An analytical hierarchy process (AHP) method is used to analyze the hierarchical relationships and calculate the relative importance of the selected RIFs. Due to the complexity and uncertainty involved in the comprehensive analysis of RIFs for the AMTS, fuzzy sets are incorporated into AHP analysis to represent and treat the epistemic uncertainty. The identified critical RIFs in this study can be used to propose specific guidance for the operations of crews on board, ship owners, and ship managers.