A method for fuzzy risk analysis based on the new similarity of trapezoidal fuzzy numbers

At present, some researchers provide a type of fuzzy risk analysis algorithms for dealing with fuzzy risk analysis problems, where the values of the evaluating items are represented by trapezoidal fuzzy numbers. In those algorithms, the main operations are two: one is arithmetic operators of the trapezoidal fuzzy numbers; the other is the similarity of the trapezoidal fuzzy numbers. However, the arithmetic operators of some algorithms do not satisfy some properties of the trapezoidal fuzzy numbers and the similarity of the trapezoidal fuzzy numbers does not coincide with the intuition of the human being. Due to this situation, in this paper, we present an efficient approach for fuzzy risk analysis based on some new arithmetic operators of the trapezoidal fuzzy numbers and propose a new similarity of the trapezoidal fuzzy numbers to deal with fuzzy risk analysis problems. At the same time, we make an experiment to use 30 sets of trapezoidal fuzzy numbers to compare the experimental results of our proposed approach with the existing similarity measures. At last, we use an example to illustrate the efficiency of the new approach.