A new ranking method for Pythagorean fuzzy numbers

Pythagorean fuzzy set (PFS), as an extension of intuitionistic fuzzy set, has received great attention in decision field. How to rank Pythagorean fuzzy numbers (PFNs) is a critical issue during the decision process. Thus, this paper focuses on the ranking method for PFNs. The main works are outlined as follows: (1) Existing ranking methods for PFNs are reviewed. Some examples are proposed to illustrate their limitations. (2) To overcome these limitations, the concepts of knowledge measure and information reliability of PFN are presented to describe the amount and quality of information of PFNs. It is comprehensive to involve the information of positive ideal point, negative ideal point and fuzzy point. (3) Motivated by the concept of relative closeness degree, an arc-length based relative closeness degree of PFN is proposed and interpreted geometrically. Moreover, the arc-length based relative closeness degree is simple and convenient for calculation. (4) A ranking method for PFNs is put forward on the basis of knowledge measure, information reliability and an arc-length based relative closeness degree.