A note on ranking generalized fuzzy numbers

The aim of this short note is to give a modification on Chen and Sanguansat's method (2011) to make the method more reasonable when the score is zero.

Abstract

Ranking fuzzy numbers plays an important role in decision making under uncertain environment. Recently, Chen and Sanguansat (2011) [Chen, S. M. & Sanguansat, K. (2011). Analyzing fuzzy risk based on a new fuzzy ranking method between generalized fuzzy numbers. Expert Systems with Applications, 38(3), (pp. 2163–2171)] proposed a method for ranking generalized fuzzy numbers. It considers the areas on the positive side, the areas on the negative side and the heights of the generalized fuzzy numbers to evaluate ranking scores of the generalized fuzzy numbers. Chen and Sanguansat's method (2011) can overcome the drawbacks of some existing methods for ranking generalized fuzzy numbers. However, in the situation when the score is zero, the results of the Chen and Sanguansat's ranking method (2011) ranking method are unreasonable. The aim of this short note is to give a modification on Chen and Sanguansat's method (2011) to make the method more reasonable.