Document Type : Research Paper

Authors

• N.A. Taghi-Nezhad
• Fatemeh Babakordi

Department of Mathematics, Faculty of Basic Science, Gonbad Kavous University, Gonbad Kavous, Iran

Abstract

In 2000, exponential trapezoidal fuzzy numbers were defined for the first time by Chen and Lie [3] without investigating the definition and properties of fuzzy numbers for them.  Therefore, in this paper first, some necessary definitions and the difference between fuzzy numbers and fuzzy quantities are presented. Then, the correctness of the definition of exponential trapezoidal fuzzy numbers is investigated. It is concluded that exponential trapezoidal fuzzy numbers do not satisfy general conditions of fuzzy numbers such as bounded amplitude and continuity. In fact, these are fuzzy quantities not fuzzy numbers. As a result, a ranking method is proposed for such quantities to be examined using common tools and test platforms that exist for ranking fuzzy quantities. Moreover, the strength and weaknesses of the method are reported.

Keywords

• Uncertainty
• Fuzzy set
• Exponential trapezoidal fuzzy numbers
• Ranking fuzzy numbers