A Revision on Area Ranking and Deviation Degree Methods of Ranking Fuzzy Numbers


Department of Industrial Engineering, K.N Toosi University of Technology, Tehran, Iran


Recently two important methods ([1],[2]) [Wang. Zh.X, Liu. Y.J, and Feng. B, “Ranking L–R fuzzy number based on deviation degree”. information science(2009). pp 2070-2077.],and [Wang.Y.M, and Luo. Y, “Area ranking of fuzzy numbers based on positive and negative ideal points.’’ Computers and Mathematics with Applications(2009). pp 1769-1779.] proposed for ranking fuzzy numbers. But we 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 is of interest.