Ranking fuzzy number based on lexicographic screening procedure

Fuzzy numbers are used for representing the numerical quantities in a vague environment. Their ranking order has been an important issue for application purposes. Most of the existing ranking methods transform a fuzzy number into a real number based on certain criteria. There is yet no method that can always give a satisfactory solution. This study pointed out that it cannot be avoided for different fuzzy numbers to be corresponding to the same real number by any type of ranking functions. Therefore, sequential screening approach would be necessary for a complete order of fuzzy numbers. We summarize the properties for a sufficient and necessary set of ranking criteria. Then, based on the ranking order of these criteria, a Lexicographical Screening Procedure is proposed, which has shown to be promising in ranking fuzzy number with efficient computation and ease of understanding. Six counterexamples of the existing methods were used for comparison.