The most crucial step of a risk assessment process that follows identifying the scope of assessment and hazards is the initial risk assessment, particularly with a risk scoring system. The Fine-Kinney method is a comprehensive method for quantitative evaluations to aid in controlling hazards. In this risk assessment method, the risk value is calculated by considering the parameters of the consequence of an accident (C), the exposure or frequency of occurrence of a hazard event that could lead to an accident (E) and the probability of a hazardous event (P). The classical Fine-Kinney method has a limitation in that it assigns an equal weight to these three parameters. Therefore, we propose a new risk assessment method incorporating a fuzzy analytic hierarchy process (FAHP) with fuzzy VIKOR (FVIKOR). FAHP was used in weighting these risk parameters derived from the Fine-Kinney method. The priority orders of hazards were determined by a FVIKOR method. The proposed method enables group decision-making in assessing hazards and uses relative importance among three risk parameters by pair-wise comparison of Buckley's FAHP. Owing to the difficulty in evaluating C, E and P, linguistic terms are used in the proposed method. In addition, a case study of the evaluation of risks in the arms industry is used to illustrate the proposed method. A comparison with the classical method and fuzzy technique for order preference by similarity of an ideal solution (FTOPSIS) is discussed. The results show that the proposed method is effective in helping stakeholders to determine the risk control policies to validate the effectiveness of their risk controls. (C) 2017 Elsevier Ltd. All rights reserved.