The ranking of fuzzy numbers plays a remarkable role in some application systems such as approximate reasoning, decision analysis, optimization and forecasting under fuzzy environments. In this paper, we propose a novel possibility degree formula of ranking generalized fuzzy numbers based on the possibility theory. The combined effects of the possibilistic mean and the variance/standard deviation on the ranking of generalized fuzzy numbers are considered. The axiomatic properties of the proposed ranking method are further verified. It is found that the possibilistic mean exhibits the dominant role as compared to the possibilistic variance or standard deviation. Some comparisons with the existing approaches are reported by carrying out lots of numerical examples. The observations reveal that the shortcomings in an existing method can be overcome. Generalized fuzzy numbers can be distinguished using a possibility degree. The developed ordering procedures of fuzzy numbers are consistent with human intuition, where the inherent uncertainty of fuzzy quantities is revealed.

模糊数的排序在一些应用系统中起着显著作用，例如在模糊环境下的近似推理，决策分析，优化和预测。本文基于可能性理论，提出了一种新的广义模糊数排序的可能性度公式。考虑了可能的均值和方差/标准差对广义模糊数排名的综合影响。所提出的排序方法的公理性质得到了进一步的验证。发现与可能性方差或标准差相比，可能性均值显示出主导作用。通过大量的数值例子，报告了与现有方法的一些比较。观察结果表明，可以克服现有方法的缺点。可以使用可能性度来区分广义模糊数。所开发的模糊数排序程序与人类的直觉相一致，揭示了模糊量的内在不确定性。