A New Algorithm for Ranking of Trapezoidal Fuzzy Numbers

Fuzzy numbers are used to represent numerical quantities in a vague environment since the measurements are imprecise in nature in this environment. Ranking fuzzy numbers is then an important issue for decision-making problems in a fuzzy environment. Most of the existing ranking methods transform a fuzzy number into a real number based on certain criteria. On the other hand, other methods define a ranking index between two fuzzy sets or between a fuzzy set and others. However, there is yet no method that can always give a satisfactory solution. In this paper, the authors propose a new algorithm for ranking of trapezoidal fuzzy numbers. This method is based on the principle that there are only four possible topological configurations when we compare two trapezoidal fuzzy numbers. Moreover, the proposed method is consistent with our intuition and, when it is necessary, takes into account the decision-maker’s risk-attitude. The paper also presents several comparative examples and an application demonstrating the usage, advantages (simplicity, flexibility, practicability, etc.) and applicability of the proposed ranking method.