Ranking of Z-Numbers Based on the Developed Golden Rule Representative Value

Abstract

Real-world decision-making is based on human cognitive information, which is characterized by fuzziness and partial reliability. In order to better describe such information, Zadeh proposed the concept of Z-number. Ranking the Z-number is an indispensable step in solving the decision-making problem under the Z-number-based information. Golden rule representative value is a new concept introduced by Yager to rank interval values. This article expands it and proposes a new golden rule representative value for fuzzy numbers, and then, apply it to the ranking of the Z-number. Some new rules involving the centroid and fuzziness of fuzzy numbers are constructed to capture the preference of decision-makers. The Takagi–Sugeno–Kang fuzzy model is used to implement these rules. The obtained Rep function is used to construct a new golden rule representative value fuzzy subset of the Z-number and associate this new fuzzy subset with a scalar value. This fuzzy subset not only implies the fuzzy aspect of the Z-number but also contains the information in the hidden probability distribution. The scalar value is regarded as the golden rule representative value of the Z-number to participate in the ranking. The proposed method greatly retains the original information of the Z-number and can overcome the shortcomings of the existing methods. Some numerical examples are used to describe the specific process of the proposed method. The comparative analysis and discussion with existing methods clarify the advantages of the proposed method.