Fuzzy risk analysis based on ranking fuzzy numbers using -cuts, belief features and signal/noise ratios

In this paper, we present a new approach for fuzzy risk analysis based on the ranking of fuzzy numbers. First, we propose a new method for ranking fuzzy numbers using the α-cuts, the belief feature and the signal/noise ratios, where α ∈ [0, 1]. The proposed method for ranking fuzzy numbers calculates the signal/noise ratio of each α-cut of a fuzzy number to evaluate the quantity and the quality of a fuzzy number, where the signal and the noise are defined as the middle-point and the spread of each α-cut of a fuzzy number, respectively. We use the value of α as the weight of the signal/noise ratio of each α-cut of a fuzzy number to calculate the ranking index of each fuzzy number. The proposed method can rank any kinds of fuzzy numbers with different kinds of membership functions. Then, we apply the proposed fuzzy ranking method to propose a fuzzy risk analysis algorithm to deal with fuzzy risk analysis problems. Because the proposed fuzzy risk analysis method considers the degrees of confidence of decision makers’ opinions, it is more flexible than the existing methods.