Failure mode and effects analysis (FMEA) has been widely applied to many industries to identify potential deteriorated problems for product design or process fabrication. Generally, the conventional FMEA prioritizes specific failure modes based on a so-called risk priority number (i.e., RPN=O*D*S), which is simply a mathematical product of three risk factors: occurrence (O), detection (D), and severity (S). Obviously, there exist several flaws for the conventional FMEA: (1) the relative importance among three risk factors is neglected, and (2) failure modes caused by different combinations of three risk factors are possible to generate the same RPN and hence the identification of their root causes becomes quite difficult in practice. As a result, a fuzzy multi-criteria decision making (MCDM) based framework that incorporates fuzzy entropy and fuzzy TOPSIS (technique for order preference by similarity to ideal solution) is presented to improve the conventional FMEA. An industrial example regarding the manufacturing process of PCB (printed circuit board) is demonstrated in this study.