Ranking fuzzy numbers with an area between the centroid point and original point

This work proposes ranking fuzzy numbers with the area between the centroid point and original point to overcome shortcomings in the coefficient of variation (CV index).

Abstract

To improve the ranking method of Lee and Li [1], Cheng [2] proposed the coefficient of variation (CV index). Shortcomings are also found in the CV index. Cheng [2] also proposed the distance method to improve the ranking method of Murakami et al. However, the distance method is not sound either. Moreover, the CV index contradicts the distance method in ranking some fuzzy numbers. Therefore, to overcome the above shortcomings, we propose ranking fuzzy numbers with the area between the centroid point and original point.