A novel fuzzy methodology applied for ranking trapezoidal fuzzy numbers and new properties

Ranking fuzzy numbers is a key tool in decision making and other fuzzy analysis. Several strategies have been proposed for this task. However, none of them is universally accepted because counter-intuitive examples appear in all cases. Very recently, a novel methodology for ordering fuzzy numbers that satisfy several human-according properties has been introduced. This procedure overcomes some drawbacks of previous techniques and it is not based on a ranking index. In this paper, due to its feasible application in computation, we show how the novel fuzzy ranking can be particularly applied to trapezoidal (and triangular) fuzzy numbers by analysing all possible cases. Hence, new properties appear. Finally, a comparison (with other existing methods) study is carried out to show the reasonability of the obtained orderings and to illustrate the advantages of the proposed methodology.