Fuzzy Risk Analysis Based On Similarity Measures Of Fuzzy Numbers

Risk is ubiquitous, which are often accompanied by varying degrees of loss, some loss is considered unacceptable; therefore, the risk analysis is particularly important. The risk factors of the most of the systems are uncertain and fuzzy, for such systems, we often use the method of fuzzy risk analysis to analyze the risk. In the fuzzy risk analysis, there is a certain type of problems that is determined to study the similarity between the fuzzy numbers. This thesis proposes two methods for fuzzy risk analysis, which is also based on the analysis of the inadequacies of the calculation method of the similarity between fuzzy numbers. One is the calculating method of the similarity between generalized fuzzy numbers; the other is the calculating methods of the similarity between interval-valued fuzzy numbers. First of all, the new calculating method of the similarity between generalized fuzzy numbers is proposed to solve problems concerning risk analysis. This method takes into account the specific differences between the two generalized fuzzy numbers, like expansion, distance of the center, height and shape and so on, at the same time proves the importance of the proposed algorithm. The superiority of the proposed algorithm will be explained through comparing with the existing calculating method of the similarity of the generalized fuzzy numbers. And then, the new calculating method of the similarity between interval-valued fuzzy numbers is proposed on basis of the similarity of the new generalized fuzzy numbers. The method takes into account the lower fuzzy numbers, upper fuzzy numbers and the similarity of X axis of interval-valued fuzzy numbers, in the meantime, proves the three importance of the proposed algorithm. Further superiority of the proposed algorithm will be summarized through comparing with the existing calculating method of the similarity between interval-valued fuzzy numbers. Finally, the algorithm of the similarity between the fuzzy numbers is applied to the risk analysis which is based on the similarity between fuzzy numbers. The feasibility, effectiveness and practicality of the proposed method are further validated by using three fuzzy risk analysis examples. The proposed risk analysis method provides a good way for the handling of fuzzy risk analysis in the future.