Fuzzy risk analysis based on interval-valued fuzzy numbers

In this paper, we present a new method for fuzzy risk analysis based on similarity measures between interval-valued fuzzy numbers. First, we present a new similarity measure between interval-valued fuzzy numbers. It combines the concepts of geometric distance, the perimeter, the height and the center-of-gravity-points of interval-valued fuzzy numbers for calculating the degree of similarity between interval-valued fuzzy numbers. We also prove some properties of the proposed similarity measure. We make an experiment to use nine sets of interval-valued fuzzy numbers to compare the experimental results of the proposed method with the existing similarity measures. The proposed method can overcome the drawbacks of the existing similarity measures. We also propose a new division operator and an interval-valued fuzzy number adjustment algorithm. Based on the proposed similarity measure, new division operator and adjustment algorithm, we present a new fuzzy risk analysis algorithm for dealing with fuzzy risk analysis problems, where the values of the evaluating items are represented by interval-valued fuzzy numbers. The proposed method provides a useful way to deal with fuzzy risk analysis problems.