A new approach for fuzzy risk analysis based on similarity measures of generalized fuzzy numbers

A new similarity measure between generalized fuzzy numbers is presented that combines the concepts of geometric distance, the perimeter and the height of generalized fuzzyNumbers for calculating the degree of similarity between summarized fuzzy numbers.

Abstract

In this paper, we present a new method for fuzzy risk analysis based on similarity measures between generalized fuzzy numbers. First, we present a new similarity measure between generalized fuzzy numbers. It combines the concepts of geometric distance, the perimeter and the height of generalized fuzzy numbers for calculating the degree of similarity between generalized fuzzy numbers. We also prove some properties of the proposed similarity measure. We make an experiment to use 15 sets of generalized 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. Based on the proposed similarity measure between generalized fuzzy numbers, 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 generalized fuzzy numbers. The proposed method provides a useful way to deal with fuzzy risk analysis problems.