Novel approach to multi-attribute group decision-making based on interval-valued Pythagorean fuzzy power Maclaurin symmetric mean operator

To distinguish any two interval-valued Pythagorean fuzzy numbers (IVPFNs), two new comparison functions, namely, the membership degree uncertainty (MU) function and the hesitation degree uncertainty (HU) function are proposed in this paper. By combining the existing score and accuracy functions with the proposed MU and HU functions, a new comparison rule for IVPFNs is obtained, whereby two different IVPFNs may be distinguished. Then, the interval-valued intuitionistic Pythagorean fuzzy power Maclaurin symmetric mean aggregation (IVPFPMSM) operator and the weighted IVIPFMSM aggregation operator are introduced to address complex multi-attribute group decision-making (MAGDM) problems involving unreasonable evaluation values and interaction among the input arguments. Moreover, a series of properties of the proposed operators are studied. Further, based on the proposed comparison method for IVPFNs and the weighted IVPFPMSM operator, we develop a new method for interval-valued Pythagorean fuzzy MAGDM problems. Finally, two illustrative examples and a comparative analysis are provided to demonstrate the effectiveness and superiority of the proposed method. Specifically, the advantage of the proposed operators in MAGDM problems is that they can eliminate bad influences of extreme evaluation values from biased decision makers and capture the interaction between attributes.