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

Subject Areas : International Journal of Industrial Mathematics

رحیم صانعی فرد ^{1 *} , رسول صانعی فرد ² , مهسا صبوری ³

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.

Received: 2012-11-22 Accepted : 2022-04-05 Published : 2020-08-01

Keywords: L-R type generalized fuzzy number, Fuzzy function, Fuzzy numbers,

Abstract :

‎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.