Multiple Attribute Decision Making Based on Power Muirhead Mean Operators Under 2-Tuple Linguistic Pythagorean Fuzzy Environment

Due to the uncertainty and complexity of socioeconomic environments and cognitive diversity of decision makers, the cognitive information over alternatives provided by decision makers is usually uncertain and fuzzy. Two-tuple linguistic Pythagorean fuzzy sets (2TLPFSs) provide useful tools to depict the uncertain and fuzzy cognitions of the decision makers over attributes. To effectively handle such common cases, in this paper, some power Muirhead mean (PMM) operator and power dual MM (PDMM) operator operators under 2TLPFS environment are proposed and investigated the methods for multiple attribute decision making(MADM) problems based on the PMM and PDMM operators with 2-tuple linguistic Pythagorean fuzzy numbers (2TLPFNs) are investigated. Firstly, some new PMM and PDMM operators to aggregate 2-tuple linguistic Pythagorean fuzzy cognitive information is developed, such as 2-tuple linguistic Pythagorean fuzzy MM (2TLPFPMM) operator, 2-tuple linguistic Pythagorean fuzzy weighted PMM (2TLPFWPMM) operator, 2-tuple linguistic Pythagorean fuzzy PDMM (2TLPFPDMM) operator, and 2-tuple linguistic Pythagorean fuzzy weighted PDMM (2TLPFNWPDMM) operator, which consider the interrelationship of 2TLPFNs, and can generate more accurate results than the existing aggregation operators. After that, the developed aggregation operator are applied to MADM with 2TLPFNs and two MADM methods are designed, which can be applied to different decision making situations. 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.