Interval-valued Pythagorean Fuzzy Frank Power Aggregation Operators based on An Isomorphic Frank Dual Triple

Abstract

Interval-valued Pythagorean fuzzy sets (PFSs), as an extension of PFSs, have strong potential in the management of complex uncertainty in real-world applications. This study aims to develop several interval-valued Pythagorean fuzzy Frank power (IVPFFP) aggregation operators with an adjustable parameter via the integration of an isomorphic Frank dual triple. First, a special automorphism on unit interval is introduced to construct an isomorphic Frank dual triple; and this triple is further applied on the definition of interval-valued Pythagorean fuzzy Frank operational laws. Second, two IVPFFP aggregation operators with the inclusion of an adjustable parameter are defined on the basis of the proposed operational laws, and several instrumental properties are then investigated. Furthermore, some limiting cases of the proposed IVPFFP operators are analyzed with respect to the varying adjustable parameter values. Finally, an IVPFFP aggregation operator-based multiple attribute group decision-making model is developed with a practical example furnished to demonstrate its feasibility and efficiency. The power that the adjustable parameter exhibits has been leveraged to affect the final decision results, and the proposed IVPFFP operators are compared with three selected aggregation operators to demonstrate their advantages provided with a practical example.

Keywords

• Interval-valued Pythagorean fuzzy numbers
• Frank dual triple
• Frank power operators