Introducing a new approach for comparing fuzzy quantities by Rank and Mode

Many methods for ranking fuzzy numbers have been proposed. The existing methods for ranking generalized fuzzy numbers based on the optimistic index () gives dierent values for comparing the numbers by using dierent values of the optimistic index () and it is the shortcoming of this method. So we introduce a new defuzzication using a crisp number for ordering and comparing the fuzzy numbers. The calculation of the proposed method is simpler and easier in comparison the other methods and it provides the correct ordering of generalized fuzzy numbers. It is shown that the proposed modication satises all the reasonable properties of fuzzy quantities (I) and (II) proposed by X. Wang, E. E. Kerre