Introducing a ‎Revised ‎‎‎Approach for Ranking Fuzzy Numbers by Rank and Mode

Document Type : Research Paper


1 Department of Mathematics‎, ‎Urmia Branch‎, ‎Islamic Azad University‎, ‎U‎rmia‎‎, ‎Iran.

2 Department of Engineering Technology, Texas Southern University, Houston, Texas, ‎USA.‎

3 Department of Mathematics‎, ‎Urmia Branch‎, ‎Islamic Azad University‎, ‎Urmia‎‎, ‎Iran.‎


‎Many methods for ranking fuzzy numbers have been proposed‎. ‎The‎ ‎existing methods for ranking generalized fuzzy numbers based on‎ ‎the optimistic index $(\alpha) $ gives different values for‎ ‎comparing the numbers by using different values of the optimistic‎ ‎index $(\alpha)$ and it is the shortcoming of this method‎. ‎So we‎ ‎introduce a new defuzzification 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 modification satisfies all the‎ ‎reasonable properties of fuzzy quantities (I) and (II) proposed by‎ ‎X‎. ‎Wang‎, ‎E‎. ‎E‎. ‎Kerre.