An improved fuzzy risk analysis by using a new similarity measure with center of gravity and area of trapezoidal fuzzy numbers

This paper is to develop a new similarity measure of generalized trapezoidal fuzzy numbers (GTFNs). Firstly, a new method to calculate the center of gravity (COG) of GTFNs is put forward. Then, based on the drawbacks of existing similarity measures, a new similarity measure is proposed by using the COGs, areas, heights and geometric distances of GTFNs. Some properties of the proposed similarity measure are investigated. Moreover, with 32 different sets of GTFNs, we make a comparison between the proposed similarity measure and the existing similarity measures. Furthermore, two fuzzy risk analysis problems are analyzed by utilizing the new similarity measure and the results indicate that it is effective to deal with fuzzy risk analysis problems.