An improved method to rank generalized fuzzy numbers with different left heights and right heights

Ranking fuzzy numbers is a very important issue in fuzzy sets theory and applications. The methods for ranking fuzzy numbers have been extensively researched and used to solve many problems. Recently, Chen et al. [11] proposed a fuzzy ranking method to calculate the areas on the negative side, the areas on the positive side and the centroid of the generalized fuzzy numbers to evaluate the ranking scores of generalized fuzzy numbers with different left heights and right heights. The method can provide us with a useful way for fuzzy risk analysis based on generalized fuzzy numbers with different left heights and right heights. However, in several situations, the ranking results of Chen et al.'s method are unreasonable. In this paper, we propose an improved method, which considers the areas of the positive side, the areas of the negative side and the spreads of generalized fuzzy numbers as the ranking factors for ranking fuzzy numbers. The proposed method not only can rank generalized fuzzy numbers with different left heights and right heights, but also overcome the drawbacks of the existing fuzzy ranking methods.