Ranking fuzzy numbers by preference ratio

We propose a ranking method for fuzzy numbers. In this method a preference function is defined by which fuzzy numbers are measured point by point and at each point the most preferred number is identified. Then, these numbers are ranked on the basis of their preference ratio. Therefore, fuzzy numbers are compared relatively and not necessarily one is preferred absolutely over the others. This method is especially designed to evaluate alternatives in multi criteria or multi-attribute decision making. The method is intuitive and can be used to discriminate between numbers easily. The method is specially tailored for triangular fuzzy numbers (TFN) and an algorithm is presented to determine the preference ratio of a pair of TFNs. We show that at most two feasible turning points exist. This fact is very helpful to make the algorithm much easier. (C) 2001 Elsevier Science B.V. All rights reserved.