An Interval-Valued Pythagorean Fuzzy Outranking Method with a Closeness-Based Assignment Model for Multiple Criteria Decision Making

The concept of interval-valued Pythagorean fuzzy (IVPF) sets is capable of handling imprecise and ambiguous information and managing complex uncertainty in real-world applications. This paper focuses on multiple criteria decision analysis involving IVPF information and proposes a new outranking decision-making method that uses a closeness-based assignment model. In contrast to the existing assignment-based methodology, the uniqueness of this paper is the consideration of uncertain information represented by IVPF values, the determination of criterion-wise precedence rankings based on a closeness-based approach, and the development of a new measure for scalar representation. First, to underlie anchored judgments in subjective decision-making processes, this paper presents a compromising concept of the closeness index with the positive-ideal and negative-ideal IVPF values to identify criterion-wise precedence ranks among alternatives. Next, this paper defines the concept of matrices of precedence frequency and contribution to provide a basis for the proposed assignment model. To overcome the difficulty of lacking nontrivial scalar representations, a useful measure is also developed to appropriately describe IVPF values. Based on a closeness-based assignment approach, a novel outranking decision-making method is proposed to transform the extended criterion-wise ranks into the ultimate priority orders of the alternatives. The proposed method is first implemented in a practical problem of selecting a bridge construction method to demonstrate its feasibility and applicability. Moreover, its practicality and effectiveness are verified through a comparative analysis with relevant assignment-based approaches. Further comparative analyses with newly developed IVPF decision-making methods are conducted for both a risk evaluation problem and an investment problem to examine the advantages of the proposed method and extend the current technique by considering distinct preference information for adapting to the particularities in practice.