A revision on area ranking and deviation degree methods of ranking fuzzy numbers

Recently two important methods [Wang Zh., X., Liu, Y.J. and Feng, B. Ranking L-R fuzzy number based on deviation degree, Information Science, pp. 2070-2077 (2009); and Wang, Y.M. and Luo, Y. Area ranking of fuzzy numbers based on positive and negative ideal points, Computers and Mathematics with Applications, pp. 1769-1779 (2009)] have been proposed for ranking fuzzy numbers. But we have found that they both have a same basic disadvantage. In this paper, after a short review on different proposed fuzzy number ranking methods, we explain the drawback on deviation degree and the area ranking methods and provide an improvement method to overcome this shortage. Our approach is based on the maximization set and minimization set methods concepts. The results show the superiority of the proposed method in comparison with other ranking methods, especially when the ranking of the inverse and the symmetry of the fuzzy numbers are of interest.