Comparison of similarity measures for generalized trapezoidal fuzzy numbers

In the last ten years, several new similarity measures for generalized trape-zoidal fuzzy numbers were proposed in the literature. These similarity measures differ in the combination of properties of fuzzy numbers that are taken into consideration (e.g. center of gravity, height, area, perimeter, distance of significant values, etc. of the compared fuzzy numbers). The performance of these similarity measures was, so far, investigated only on several specifically chosen examples. A thorough comparison of the performance of these different similarity measures is still not available in the literature. This paper investigates the relationships between the new similarity measures using a numerical experiment. The effect of the different heights of the compared generalized fuzzy numbers is also considered. As such, the paper provides first insights into the shared features of the similarity measures.