A Possibility Theory-Based Approach to the Ranking of Generalized Fuzzy Numbers

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.