One of the problems of based models on data envelopment analysis (DEA) for Ranking preference voting systems is that it allows each alternative have its own weight vector. Therefore, alternatives are evaluated with different weight vectors. In this study, we propose a model based on Fuzzy logic to solve the weaknesses of the previous models. This model is based on the solving of multi-objective programming models with the help of Fuzzy logic, by this way it providing a vector of common weights, and finally, we can rank the alternatives.

Many Ranking methods have been proposed so far. However, there is not any method which can always give a satisfactory solution for every situation. In this paper, we propose a method for Ranking Fuzzy numbers based on the distance method and compare the results with other Ranking methods in some examples.

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.

Ranking Fuzzy numbers(FNs) was a critical issue in Fuzzy computing field. Generally, triangular FNs, trapezoidal FNs, and even interval-valued FNs(IVFNs) were often expressed in Ranking. However, Ranking intuitionistic FNs(IFNs) were less mentioned due to the complicated components in membership functions. Herein, we will develop Fuzzy binary relation that is an extended Fuzzy preference relation(EFPR) to express the preference degree of two IFNs, and then the relation is improved to be a relative preference relation(RPR) used to rank a set of IFNs. Since EFPR on IFNs is a total ordering relation, RPR will be also a total ordering relation. Based on belonging and non-belonging components of membership functions in IFNs, using EFPR being also Fuzzy preference relation(FPR) is suitable to compare FNs on pairwise, but time complexity on Fuzzy operation of comparison computing is complicated. Hence, RPR is developed to avoid comparing on pairwise. Through yielding RPR values for a set of IFNs, IFNs are effectively and efficiently ranked to utilize related decision-making problems.

In this work, we propose an approach for computing the compromised solution of an LR Fuzzy linear system by using of a Ranking function when the coefficient matrix is a crisp m´n matrix. To do this, we use expected interval to find an LR Fuzzy vector, X~, such that the vector Â(AX~) has the least distance from Â(b~) in 1-norm and the 1-cut of X~ satisfies the crisp linear system AX=b. Then, we solve the constrained LP-problem by using LINGO 11 software package and obtain optimal Fuzzy number solution. Finally, we illustrate the proposed method by solving two numerical examples.

In this paper, a novel approach for Ranking Fuzzy numbers based on the angle measure is introduced. Several left and right spreads at each chosen a-levels of Fuzzy numbers is used to determine center of mass points (CMPs) and then, the angels between the CMPs and the horizontal axis is calculated. The total angle is determined by averaging the computed angles and finally, the novel method is compared with other methods by solving some numerical examples.