Failure modes and effects analysis (FMEA) is a widely used engineering tool in the fields of the design of a product or a process to improve its quality or performance by prioritizing potential failure modes in terms of three risk factors―severity, occurrence, and detection. In a classical FMEA, the risk priority number is obtained by multiplying the three values in 10 score scales which are evaluated for the three risk factors. However, the drawbacks of the classical FMEA have been mentioned by many previous researchers. As a way to overcome these difficulties, this paper suggests the ELECTRE III that is a representative technique among outranking models. Furthermore, fuzzy linguistic variables are included to deal with ambiguous and imperfect evaluation process. In addition, when the importances for the three risk factors are obtained, the entropy method is applied. The numerical example which was previously studied by Kutlu and Ekmek‡ioğlu(2012), who suggested the fuzzy TOPSIS method along with fuzzy AHP, is also adopted so as to be compared with the results of their research. Finally, after comparing the results of this study with that of Kutlu and Ekmek‡ioğlu(2012), further possible researches are mentioned.