Failure mode, effects, and criticality analysis (FMECA) is a proactive quality tool that allows the identification and prevention of the potential failure modes of a process or product. In a conventional FMECA, for each failure mode, three risk parameters, namely frequency, non-detection, and severity are evaluated and a risk priority number (RPN) is calculated by multiplying these parameters to assess one signal criticality. However, in many cases, it suffers from some shortcomings regarding the decision-making and the situation where the information provided is ambiguous or uncertain. This paper describes a new fuzzy multi-criticality approach for improving the use of FMECA by treating FMECA as a fuzzy multi-criteria optimization model. The new approach bases on replacing the calculation of a single criticality with a fuzzy inference system for improving the criticality evaluations which offers five partial criticalities that efficiently and separately calculate the impact of a failure on the environment, personnel, production, equipment, and management. In addition, an analytical hierarchy method (AHP) is used to calculate the priorities weights for each partial criticality and construct a criticality matrix in order to improve the relevance of decision-making. Furthermore, a real case of LPG storage system for ZCINA Hassi Messaoud in Algeria is provided to illustrate the practical implementation of the suggested approach and extremely shows the pertinence of the suggested fuzzy model as decision-making tools in preventing industrial risks with providing encouraging results regarding the criticality estimation and improve decision-making by prioritizing “preventive –corrective actions” and determine the efficient action for each partial criticality to control the risk effectively.