Nowadays, global and local safety and security are gaining increased importance, in terms of product and process safety as well. The most important and widespread method for risk analysis are Failure Mode and Effect Analysis (FMEA), and its predecessor Failure Mode Effects and Criticality Analysis (FMECA), which are used for a wide range of purposes. However, traditional FMEA and FMECA have shortcomings as well, which need to be avoided to gain a complex, correct analysis. In our work, our goal is to give an overview about the non-conventional Failure Mode and Effect methods, which are related to fuzzy logic. Three wide fields are taken into consideration in our study: Multi-Criteria Decision Making methods, Mathematical Programming and Artificial Intelligence approaches. These approaches tend to solve the major shortcomings of FMEA in handling risk analysis. In our work, we sort out the advantages and possible disadvantages of the mentioned analysis types.