A novel method to rank fuzzy numbers using the developed golden rule representative value

摘要

Ranking fuzzy numbers is an important subject of fuzzy set theory, which has been widely studied and applied to many practical problems. However, the previous fuzzy number ranking methods have some weaknesses, such as incomplete ranking objects, complicated calculations, and ignoring interpretability. To overcome these weaknesses and develop a ranking method that performs better in all aspects, the concept of the golden rule representative value is used. The golden rule representative value was first introduced by Yager to solve the order of interval values. This paper expands it and proposes a novel fuzzy number ranking method based on the developed golden rule representative value. The centroid point and area of fuzzy numbers are considered, and some new rules are formulated to capture the preference of the decision-maker. The TSK fuzzy model is used to model the rules. The constructed Rep function associates each fuzzy number with a scalar value. By comparing these scalar values, we get the ranking order of fuzzy numbers. The proposed ranking method is simple to use and can overcome the shortcomings of existing methods. Some specific numerical examples are used to illustrate the property of the proposed method, and the corresponding explanations show the interpretability of the ranking process. The comparative experiment with the existing ranking method shows the advantages of the proposed method. An application example of fuzzy risk analysis proves the effectiveness of the proposed method.