Failure modes, effects, and criticality analysis (FMECA) is a qualitative risk analysis method widely used in various industrial and service applications. Despite its popularity, the method suffers from several shortcomings analyzed in the literature over the years. The classical approach to obtain the failure modes’ risk level does not consider any relative importance between the risk factors and may not necessarily represent the real risk perception of the FMECA team members, usually expressed by natural language. This paper introduces the application of Type-I fuzzy inference systems (FIS) as an alternative to improve the failure modes’ risk level computation in the classic FMECA analysis and its use in cyber-power grids. Our fuzzy-based FMECA considers first a set of fuzzy variables defined by FMECA experts to embody the uncertainty associated with the human language. Second, the “seven plus or minus two” criterion is used to set the number of fuzzy sets to each variable, forming a rule base consisting of 125 fuzzy rules to represent the risk perception of the experts. In the electrical power systems framework, the new fuzzy-based FMECA is utilized for reliability analysis of cyber-power grid systems, assessing its benefits relative to a classic FMECA. The paper provides the following three key contributions: (1) representing the uncertainty associated with the FMECA experts using fuzzy sets, (2) representing the FMECA experts’ reasoning and risk perception through fuzzy-rule-based reasoning, and (3) applying the proposed fuzzy approach, which is a promissory method to accurately define the prioritization of failure modes in the context of reliability analysis of cyber-power grid systems.