Arctic marine traffic is increasing as ice conditions change, creating greater risks of vessel collisions and groundings. To address the need for more reliable quantitative risk evaluation, this paper presents a new safety risk index tailored to Arctic maritime operations. The index integrates fuzzy-logic linguistic scoring with Multi-Criteria Decision-Making (MCDM) methods to convert expert judgements into a consistent numerical measure. The methodology involves defining qualitative criteria, assigning fuzzy membership functions, constructing expert-driven rule bases, and aggregating results through an MCDM approach. These components are calibrated using expert workshops to improve accuracy. Validation using historical Arctic collision and grounding cases shows that the index reduces false-negative alerts compared with traditional threshold-based tools. Sensitivity analysis identifies which criteria most strongly influence risk outcomes. Overall, the proposed index provides a more objective, transparent, and operationally useful assessment framework to support planners and bridge teams navigating Arctic waters.