Ranking fuzzy numbers with an area method using radius of gyration

Ranking fuzzy numbers plays an very important role in linguistic decision making and some other fuzzy application systems. Many methods have been proposed to deal with ranking fuzzy numbers. Chu pointed out some shortcomings of the existing distance method and proposed to rank the fuzzy numbers with the area between the centroid point and original point. However, drawbacks are also found in the area method. For example, it cannot rank fuzzy numbers when some fuzzy numbers have the same centroid point. In this paper, we propose a modified area method to rank fuzzy numbers. The modified method can effectively rank various fuzzy numbers and their images. We also used some comparative examples to illustrate the advantage of the proposed method.