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In this paper, we expand the Muirhead mean (MM) operator and dual MM (DMM) operator with 2-tuple linguistic Pythagorean fuzzy numbers (2TLPFNs) to propose the 2-tuple linguistic Pythagorean fuzzy MM (2TLPFMM) operator, 2-tuple linguistic Pythagorean fuzzy weighted MM (2TLPFWMM) operator, 2-tuple linguistic Pythagorean fuzzy DMM (2TLPFDMM) operator and 2-tuple linguistic Pythagorean fuzzy weighted DMM (2TLPFNWDMM) operator. Based on the proposed operators and built models, two methods are developed to solve the MADM problems with 2TLPFNs and the validity and advantages of the proposed method are analyzed by comparison with some existing approaches. The method proposed in this paper can effectively handle the MADM problems in which the attribute information is expressed by 2TLPFNs, the attributes’ weights are completely known, and the attributes are interactive. Finally, an example for green supplier selection is used to show the proposed methods.

Multiple attribute decision making based on Muirhead mean operators under 2-tuple linguistic Pythagorean fuzzy environment