Models for Multiple Attribute Decision Making with Interval-Valued Pythagorean Fuzzy Muirhead Mean Operators and Their Application to Green Suppliers Selection

In this paper, we extend MM operator and dual MM (DMM) operator to process the interval-valued Pythagorean fuzzy numbers (IVPFNs) and then to solve the MADM problems. Firstly, we develop some interval-valued Pythagorean fuzzy Muirhead mean operators by extending MM and DMM operators to IVPFNs. Then, we prove some properties and discuss some special cases with respect to the parameter vector. Moreover, we present some new methods to deal with MADM problems with the IVPFNs based on the proposed MM and DMM operators. Finally, we verify the validity and reliability of our methods by using an application example for green supplier selections, and analyse the advantages of our methods by comparing it with other existing methods.