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 generalizedfuzzy numbers based on the optimistic index () gives di erent values for comparing the numbers by usingdierent values of the optimistic index () and it is the shortcoming of this method. so we introduce a newdefuzzication using a crisp number for ordering and comparing the fuzzy numbers. the calculation of theproposed method is simpler and easier in comparison the other methods and it provides the correct orderingof generalized fuzzy numbers. it is shown that the proposed modication satises all the reasonable propertiesof fuzzy quantities (i) and (ii) proposed by x. wang, e. e. kerre [18, 19].