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The overall quality evaluation of operation personnel helps contain site safety accidents, in this study, we proposed a combination of the Pythagorean 2-tuple linguistic fuzzy set and qualitative flexible multiple criteria (QUALIFLEX) method to evaluate comprehensive quality of operation personnel in engineering projects, Pythagorean 2-tuple linguistic fuzzy numbers to express decision makers’ evaluation on each scheme with original QUALIFLEX approach to decision making process. In the end, an example of the performance evaluation of operation personnel in the engineering project is provided to test the applicability and practicability of the method, comparison analysis for further elaboration.

The risk assessment of science and technology projects could be regarded as a classical multiple attribute group decision-making (MAGDM) issue. The Pythagorean fuzzy sets (PFSs) can fully describe the uncertain information for the risk assessment of science and technology projects. Furthermore, the classical TODIM method based on the cumulative prospect theory (CPT-TODIM) is built, which is a selectable method in reflecting the DMs’ psychological behavior. Thus, in this paper, the Pythagorean fuzzy CPT-TODIM (PF-CPT-TODIM) method is proposed for MAGDM issue. At the same time, it is enhancing rationality to get the weight information of attributes by using the entropy weight method under PFSs. And focusing on hot issues in contemporary society, this article applies the discussed method to risk assessment of science and technology projects, and demonstrates risk assessment model of science and technology projects based on the proposed method. Finally, through comparing the outcome of comparative analysis, we conclude that this improved approach is acceptable.

The green supplier selection could be regarded as a classical multiple attribute group decision making (MAGDM) issue. The interval-valued Pythagorean fuzzy set (IVPFSs) can fully describe the uncertain information for the risk assessment of science and technology projects. Furthermore, the classical TODIM method based on the cumulative prospect theory (CPT-TODIM) is built, which is a selectable method in reflecting the decision makers’ psychological behavior. Thus, in this paper, the interval-valued Pythagorean fuzzy CPT-TODIM (IVPF-CPT-TODIM) method is proposed for MAGDM issue. At the same time, it is enhancing rationality to get the weight information of attributes by using the entropy weight method under IVPFSs. And focusing on hot issues in contemporary society, this article applies the discussed method to green supplier selection, and demonstrates risk assessment model of science and technology projects based on the IVPF-CPT-TODIM method. Finally, through comparing the outcome of comparative analysis, we conclude that this improved approach is acceptable.

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.

Financial management performance evaluation (FMPE) has a significant effect on the identifying an investment chance. We can usually consider FMPE as a multiple attribute group decision making (MAGDM) issue, and the MAGDM method is needed to address it. Uncertainty may be one of the significant factors which could influence the process of MAGDM. In order to handle the uncertainty of group decision-making issues, MAGDM approaches along with 2-tuple linguistic Pythagorean fuzzy sets (2TLPFSs) have been designed. In this essay, CODAS method is extended to 2TLPFSs to tackle MAGDM issues. Linguistic variables and 2TLPFSs are also used to extend the CODAS method. An application of the presented 2-tuple linguistic Pythagorean fuzzy CODAS (2TLPF-CODAS) method to a case study of FMPE problem with 2-tuple linguistic Pythagorean fuzzy numbers (2TLPFNs) is given. To confirm the results, a comparative analysis between the fuzzy CODAS and 2TLPF-TODIM is performed. The results of the comparison illustrate that the presented 2TLPF-CODAS method offers effective and steady results.

In this paper, we investigate the multiple attribute decision making problems with Pythagorean 2-tuple linguistic information. Then, we utilize power average and power geometric operations to develop some Pythagorean 2-tuple linguistic power aggregation operators: Pythagorean 2-tuple linguistic power weighted average (P2TLPWA) operator, Pythagorean 2-tuple linguistic power weighted geometric (P2TLPWG) operator, Pythagorean 2-tuple linguistic power ordered weighted average (P2TLPOWA) operator, Pythagorean 2-tuple linguistic power ordered weighted geometric (P2TLPOWG) operator, Pythagorean 2-tuple linguistic power hybrid average (P2TLPHA) operator and Pythagorean 2-tuple linguistic power hybrid geometric (P2TLPHG) operator. The prominent characteristic of these proposed operators are studied. Then, we have utilized these operators to develop some approaches to solve the Pythagorean 2-tuple linguistic multiple attribute decision making problems. Finally, a practical example for enterprise resource planning (ERP) system selection is given to verify the developed approach and to demonstrate its practicality and effectiveness.

In this paper, we expand the generalised Heronian mean (GHM) operator, generalised weighted Heronian mean (GWHM), geometric Heronian mean (GHM) operator, and weighted geometric Heronian mean (WGHM)...

In today’s world, with the advancement of technology, several emerging technologies are coming. Faced with massive emerging technologies which are the component of the technology pool, how to identify the commercial potential of emerging technologies in theory and practice is an important problem. The scientific approach to the selection of these emerging technologies is one of the main objectives of the research. In this paper, we extend Muirhead mean (MM) operator and dual MM (DMM) operator to process the Pythagorean fuzzy numbers (PFNs) and then to solve the multiple attribute decision making (MADM) problems. Firstly, we develop some Pythagorean fuzzy Muirhead mean operators by extending MM and DMM operators to Pythagorean fuzzy information. 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 PFNs based on the proposed MM and DMM operators. Finally, we verify the validity and reliability of our methods by using an application example for potential evaluation of emerging technology commercialization, and analyze the advantages of our methods by comparing with other existing methods.

To fuse the information in dual-hesitant Pythagorean fuzzy sets (DHPFSs) more effectively, in this paper, some dual hesitant Pythagorean fuzzy Hamy mean (DHPFHM) operators, which can consider the relationships between being fused arguments, are defined and studied. Afterward, the defined aggregation operators are used to multiple attribute decision-making (MADM) with dual-hesitant Pythagorean fuzzy elements (DHPFEs), and the MADM decision-making model is developed. In accordance with the defined operators and the built model, the dual-hesitant Pythagorean fuzzy weighted Hamy mean (DHPFWHM) operator and the dual-hesitant Pythagorean fuzzy weighted dual Hamy mean (DHPFWDHM) operator are applied to deal with green supplier selection in supply chain management, and the availability and superiority of the proposed operators are analyzed by comparing with some existing approaches. The method presented in this paper can effectually solve the MADM problems, which the decision-making information is expressed by DHPFEs and the attributes are interactive.

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. Dual hesitant Pythagorean fuzzy sets (DHPFSs) provide a useful tool to depict the uncertain and fuzzy cognitions of the decision makers over attributes. To effectively handle such common cases, in this paper, some Bonferroni mean (BM) operators under DHPFS environment are proposed and some methods for multiple attribute decision-making (MADM) problems based on the BM operators with dual Pythagorean hesitant fuzzy numbers (DHPFNs) are investigated. Firstly, some new BM operators to aggregate dual Pythagorean hesitant fuzzy cognitive information are developed, which consider the interrelationship of DHPFNs, and can generate more accurate results than the existing dual Pythagorean hesitant fuzzy aggregation operators. Then, the developed aggregation operator is applied to MADM with DHPFNs 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 DHPFNs and the validity and advantages of the proposed method are analyzed by comparison with some existing approaches. The methods proposed in this paper can effectively handle the MADM problems in which the attribute information is expressed by DHPFNs, the attributes’ weights are completely known, and the attributes are interactive.

Green supply chain management is a strategy which strengthens and integrates environmental consideration into whole supply chain. The green strategic supplier plays an important role in the implementation of green supply chain strategy. In the selection methodology of a strategic green supplier, some special requirements are needed which are different from the traditional supplier selection practices. In this paper, we combine the generalized weighted BM operator with Pythagorean 2-tuple linguistic numbers to propose the generalized Pythagorean 2-tuple linguistic-weighted Bonferroni mean operator, and then the multiple attribute decision-making methods are developed based on this operator. Finally, we use an example for green supplier selection to illustrate the multiple attribute decision-making process of the proposed methods.

In this article, we combine some fundamental theories of the Pythagorean 2-tuple linguistic sets (P2TLSs) with EDAS method and design the Pythagorean 2-tuple linguistic number (P2TLN) EDAS (P2TLN-EDAS) method for multiple attribute group decision making (MAGDM) issue. Firstly, the basic concepts of P2TLSs are introduced. Next, two aggregation operators of P2TLN are defined, and then the calculation steps of EDAS method are listed briefly. Furthermore, P2TLN-EDAS method is given for MAGDM problems and computing steps are proposed in detail. Finally, a computational example related to construction safety assessment is used to expound the effectiveness of the designed method. Meanwhile, we also carried out some comparative analysis between P2TLN-EDAS method and P2TLWA/P2TLWG operators and another P2TLN-TODIM method. The results show that P2TLN-EDAS method derives the same best alternative as P2TLWA, P2TLWG operators and P2TLN-TODIM method. First published online 24 September 2020

Low-carbon tourism plays the increasingly significant role in carbon emission reduction and natural environmental protection. The choice of low-carbon tourist destination (LCTD) often involves the multiple attributes or criteria and can be regarded as the corresponding multiple attribute group decision making (MAGDM) issues. Since the Pythagorean fuzzy sets (PFSs) could well depict uncertain information or fuzzy information and cope with the LCTD selection, thus this essay develops a framework to tackle such MAGDM issues under the Pythagorean fuzzy environment. In this essay, due to few methods can compare with different alternatives along with their advantages from designed attributes, therefore, to overcome this challenge, the taxonomy method is utilized to integrate with PFSs. What’s more, the entropy method is also utilized to determine the attribute weights. Eventually, an application related to LCTD selection and some comparative analysis have been given to demonstrate the superiority of the designed method. The results illustrate that the designed framework is useful for identifying optimal tourist destination among the potential tourist destinations.

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.

Supplier selection in medical instrument industries is a classical multiple attribute group decision making (MAGDM) problem. The Pythagorean 2-tuple linguistic sets (P2TLSs) can reflect uncertain or fuzzy information well and solve the supplier selection in medical instrument industries, and the original Taxonomy is very appropriate for comparing different alternatives with respect to their advantages from studied attributes. In this study, we present an algorithm that combines Pythagorean 2-tuple linguistic numbers (P2TLNs) with the Taxonomy method, where P2TLNs are applied to express the evaluation of decision makers on alternatives. Relying on the Pythagorean 2-tuple linguistic weighted average (P2TLWA) operator or Pythagorean 2-tuple linguistic weighted geometric (P2TLWG) operator to fuse P2TLNs, the new general framework is established for Pythagorean 2-tuple linguistic multiple attribute group decision making (MAGDM) under the classical Taxonomy method. Ultimately, an application case for supplier selection in medical instrument industries is designed to test the novel method&rsquo, s applicability and practicality and a comparative analysis with three other methods is used to elaborate further.

For this paper, to consider both Bonferroni mean (BM) operator and two-tuple linguistic Pythagorean fuzzy numbers (2TLPFNs), we combine the weighted BM (WBM) operator, the generalized WBM (GWBM) operator, and the dual GWBM operator with 2TLPFNs to propose the two-tuple linguistic Pythagorean WBM (2TLPFWBM) operator, the 2TLPFWGBM operator, the generalized 2TLPFWBM (G2TLPFWBM) operator, the generalized 2TLPFWGBM operator, the dual G2TLPFWBM operator, and the dual G2TLPFWGBM operator. Then, some MADM procedures are developed based on these operators. At last, an applicable example for a safety assessment of construction project is given.

Interval-valued Pythagorean fuzzy (IVPF) set is one the successful extension of the existing theories for handling the uncertainties during the decision-making process. Under that environment, various aggregation operators have been developed by the authors to aggregate the different preferences of the decision makers under the different attributes. But these studies have conducted under the assumption that their corresponding pairs are independent and don’t consider the interaction between the pairs of the membership degrees. In this paper, these conditions have been relaxed by considering the interrelationship between the different inputs by using Maclaurin symmetric mean (MSM) operator. Further, based on the input and MSM operator, we proposed two aggregation operators namely, IVPF Maclaurin symmetric mean and IVPF weighted Maclaurin symmetric mean operators and studied their desirable properties. A decision-making method based on these operators has been discussed for solving the decision-making problems under IVPF set environment. Finally, an illustrative example and a comparative analysis have been presented to demonstrate the proposed approach.

In recent years, the environmental problems in China have become more and more serious, for example, resource depletion, environmental pollution, ecological imbalance, and so on. At the same time, the laws and regulations about the environmental protection in the world are constantly introduced, the academic research about the environmental issues is also increasing, more and more consumers show concern for the green products, and the restrictions of the “green trade barrier”in the international to the export products in China enterprises must pay attention to the influence of their behavior on the environment in pursuit of economic efficiency. In this context, the green supply chain management (GSCM) emerges. GSCM theory first appeared in some foreign countries, and started later in China. Compared with some developed countries, the GSCM theory in China is still not mature. From the source speaking, there is lack of a complete GSCM system. In this paper, we combine the generalized weighted Bonferroni mean (GWBM) operator, generalized weighted geometric Bonferroni mean (GWGBM) operator, dual GWBM operator, and dual GWGBM operator with Pythagorean 2-tuple linguistic numbers to propose the generalized Pythagorean 2-tuple linguistic WBM (GP2TLWBM) operator, generalized Pythagorean 2-tuple linguistic WGBM (GP2TLWGBM) operator, dual GP2TLWBM (DGP2TLWBM) operator, and dual GP2TLWGBM (DGP2TLWGBM) operator, and then, the multiple attribute decision-making (MADM) methods are developed based on DGP2TLWBM and DGP2TLWGBM operators. Finally, we use an example for green supplier selection to prove the MADM process of the proposed algorithms.

In this paper, we utilize power aggregation operators to develop some Pythagorean fuzzy power aggregation operators: Pythagorean fuzzy power average operator, Pythagorean fuzzy power geometric operator, Pythagorean fuzzy power weighted average operator, Pythagorean fuzzy power weighted geometric operator, Pythagorean fuzzy power ordered weighted average operator, Pythagorean fuzzy power ordered weighted geometric operator, Pythagorean fuzzy power hybrid average operator, and Pythagorean fuzzy power hybrid geometric operator. The prominent characteristic of these proposed operators are studied. Then, we have utilized these operators to develop some approaches to solve the Pythagorean fuzzy multiple attribute decision-making problems. Finally, a practical example is given to verify the developed approach and to demonstrate its practicality and effectiveness.

The Hamacher product is a t-norm and the Hamacher sum is a t-conorm. They are good alternatives to the algebraic product and the algebraic sum, respectively. Nevertheless, it seems that most of the existing hesitant fuzzy aggregation operators are based on algebraic operations. In this paper, we utilize Hamacher operations to develop some Pythagorean hesitant fuzzy aggregation operators: Pythagorean hesitant fuzzy Hamacher weighted average operator, Pythagorean hesitant fuzzy Hamacher weighted geometric operator, Pythagorean hesitant fuzzy Hamacher ordered weighted average operator, Pythagorean hesitant fuzzy Hamacher ordered weighted geometric operator, Pythagorean hesitant fuzzy Hamacher hybrid average operator, and Pythagorean hesitant fuzzy Hamacher hybrid geometric operator. The prominent characteristics of these proposed operators are studied. Then, we utilize these operators to develop some approaches for solving the Pythagorean hesitant fuzzy multiple-attribute decision-making problems. Finally, a practical example is given to verify the developed approach and to demonstrate its practicality and effectiveness.

In this paper, we investigate the multiple attribute decision making (MADM) problem based on the Hamacher aggregation operators with dual Pythagorean hesitant fuzzy information. Then, motivated by the ideal of Hamacher operation, we have developed some Hamacher aggregation operators for aggregating dual hesitant Pythagorean fuzzy information. The prominent characteristic of these proposed operators are studied. Then, we have utilized these operators to develop some approaches to solve the dual hesitant Pythagorean fuzzy multiple attribute decision making problems. Finally, a practical example for supplier selection in supply chain management is given to verify the developed approach and to demonstrate its practicality and effectiveness.

The Maclaurin symmetric mean (MSM) operator is a classical mean type aggregation operator used in modern information fusion theory, which is suitable to aggregate numerical values. The prominent characteristic of the MSM operator is that it can capture the interrelationship among the multiinput arguments. In this paper, we extend MSM to Pythagorean fuzzy environment to propose the Pythagorean fuzzy Maclaurin symmetric mean and Pythagorean fuzzy weighted Maclaurin symmetric mean operators. Then, some desirable properties and special cases of these operators are discussed in detail. Finally, a numerical example is provided to illustrate the feasibility of the proposed methods and deliver a comparative analysis.

On account of the indeterminacy and subjectivity of decision makers (DMs) in complexity decision-making environments, the evaluation information over alternatives presented by DMs is usually fuzzy and ambiguous. As the generalization of intuitionistic fuzzy sets (IFSs), the Pythagorean fuzzy set (PFS) is more useful in expressing fuzzy and ambiguous information. Meanwhile, in order to consider human hesitance, dual hesitant Pythagorean fuzzy sets (DHPFSs) are presented, which can be more valid for handling real multiple attribute decision-making (MADM) problems. To fuse the information in DHPFSs more effectively, in this article, some dual hesitant Pythagorean fuzzy Heronian mean operators, which can consider the relationships between arguments being fused, are defined and studied. Evidently, the new proposed operators can obtain more exact results than other existing methods. In addition, some important properties of these Heronian mean (HM) operators are discussed. Subsequently, the defined aggregation operators are used in MADM with dual hesitant Pythagorean fuzzy numbers (DHPFNs), and the MADM model is developed. In accordance with the defined operators and the built model, the dual hesitant Pythagorean fuzzy generalized weighted Heronian mean (DHPFGWHM) operator and dual hesitant Pythagorean fuzzy generalized geometric weighted Heronian mean (DHPFGGWHM) operator are applied to deal with the green supplier selection in supply chain management, and the availability and superiority of the proposed operators are analyzed by comparing them with some existing approaches. The method presented in this paper can effectively solve the MADM problems in which the decision-making information is expressed by DHPFNs and the attributes are interactive.

Interval-valued Pythagorean fuzzy numbers (IVPFNs) can easily describe the incomplete and indeterminate information by degrees of membership and non-membership, and the Hamy mean (HM) operator and dual HM (DHM) operators are a good tool for dealing with multiple attribute decision making (MADM) problems because it can capture the interrelationship among the multi-input arguments. Motivated by the studies regarding the HM operator and dual HM operator, we expand the HM operator and dual HM (DMM) operator to process the interval-valued Pythagorean fuzzy numbers (IVPFNs) and then to solve the MADM problems. Firstly, we propose some HM and DHM operators with IVPFNs. Moreover, we present some new methods to solve MADM problems with the IVPFNs. Finally, an applicable example is given.

The Hamy mean (HM) operator, as a useful aggregation tool, can capture the correlation between multiple integration parameters, and the 2-tuple linguistic Pythagorean fuzzy numbers (2TLPFNs) are a special kind of Pythagorean fuzzy numbers (PFNs), which can easily describe the fuzziness in actual decision making by 2-tuple linguistic terms (2TLTs). In this paper, to consider both Hamy mean (HM) operator and 2TLPFNs, we combine the HM operator, weighted HM (WHM) operator, dual HM (DHM) operator, and dual WHM (DWHM) operator with 2TLPFNs to propose the 2-tuple linguistic Pythagorean fuzzy HM (2TLPFHM) operator, 2-tuple linguistic Pythagorean fuzzy WHM (2TLPFWHM) operator, 2-tuple linguistic Pythagorean fuzzy DHM (2TLPFDHM) operator and 2-tuple linguistic Pythagorean fuzzy DWHM (2TLPFDWHM) operator. Then some multiple attribute decision making (MADM) procedures are developed based on these operators. At last, an applicable example for green supplier selection is given.

The aging trend of China&rsquo, s population is increasing, and the pension problem is becoming increasingly prominent. The pension mode provided by the government alone can no longer meet the social demand, and the government&rsquo, s purchase of home-based care services from social organizations has become a new trend. In order to improve the efficiency and quality of pension services, a reasonable performance evaluation model needs to be established. Performance evaluations of home-based elderly-care services purchased by the government are problematic as a result of multiple-attribute group decision-making (MAGDM), as the problems are not single-attribute or single-expert issues. The extended TODIM not only integrates the advantages of cumulative prospect theory (CPT) into a consideration of the psychological factors of DMs, but also retains the superiority of the classical TODIM in relative dominance. The Pythagorean 2-tuple linguistic sets (P2TLSs) could easily depict qualitative assessment information related to the government&rsquo, s purchase of home-based care services. Thus, in this paper, we extend the TODIM method based on the cumulative prospect theory (CPT) to the Pythagorean 2-tuple linguistic sets (P2TLSs) and propose a Pythagorean 2-tuple linguistic CPT-TODIM (P2TL-CPT-TODIM) method for MAGDM. The P2TL-CPT-TODIM method was proven superior to the classical one through a case study that included a performance evaluation of a home-based elderly-care service purchased by the government. Meanwhile, a comparison with the P2TL-CPT-TODIM method was performed to demonstrate the stability and effectiveness of the designed method.

The evaluation of the financial performance of universities is conducive to the sustainable development of universities. Based on this, we extend the traditional CODAS (COmbinative Distance-based ASsessment) method to the Pythagorean 2-tuple linguistic fuzzy environment and propose a P2TL-CODAS model to evaluate the financial management performance of universities. Firstly, we briefly describe the definition, the score function, accuracy function, operational laws and the distance calculating method of P2TLSs. Next, two aggregation operators of P2TL including Pythagorean 2-tuple linguistic weighted averaging (P2TLWA) operator and Pythagorean 2-tuple linguistic weighted geometric (P2TLWG) operator are also introduced to fuse overall Pythagorean 2-tuple linguistic evaluation information. Then the steps of CODAS method are depicted briefly. Moreover, we use linguistic Pythagorean 2-tuple linguistic fuzzy numbers to extend the CODAS method. The P2TL-CODAS model is established and all computing steps are simply presented. Furthermore, we apply the proposed method to evaluate the financial management performance about five universities. Finally, a comparison between P2TL-CODAS method and P2TL-TODIM method is made to demonstrate the stability of the new method. The results show that the proposed method has unique advantages.

The Maclaurin symmetric mean (MSM) operator is a classical mean type aggregation operator used in modern information fusion theory, which is suitable to aggregate numerical values. The prominent characteristic of the MSM operator is that it can capture the interrelationship among multi-input arguments. Motivated by the ideal characteristic of the MSM operator, in this paper, we expand the MSM operator, generalized MSM (GMSM), and dual MSM (DMSM) operator with interval-valued 2-tuple linguistic Pythagorean fuzzy numbers (IV2TLPFNs) to propose the interval-valued 2-tuple linguistic Pythagorean fuzzy MSM (IV2TLPFMSM) operator, interval-valued 2-tuple linguistic Pythagorean fuzzy weighted MSM (IV2TLPFWMSM) operator, interval-valued 2-tuple linguistic Pythagorean fuzzy GMSM (IN2TLPFGMSM) operator, interval-valued 2-tuple linguistic Pythagorean fuzzy weighted GMSM (IV2TLPFWGMSM) operator, interval-valued 2-tuple linguistic Pythagorean fuzzy DMSM (IN2TLPFDMSM) operator, Interval-valued 2-tuple linguistic Pythagorean fuzzy weighted DMSM (IV2TLPFWDMSM) operator. Then the multiple attribute decision making (MADM) methods are developed with these three operators. Finally, an example of green supplier selection is used to show the proposed methods.

In this paper, we investigate multiple-attribute decision-making (MADM) with Pythagorean 2-tuple linguistic numbers (P2TLNs). Then, we combine the weighted Bonferroni mean (WBM) operator and weighted geometric Bonferroni mean (WGBM) operator with P2TLNs to propose the Pythagorean 2-tuple linguistic WBM (P2TLWBM) operator and Pythagorean 2-tuple linguistic WGBM (P2TLWGBM) operator; MADM methods are then developed based on these two operators. Finally, a practical example for green supplier selection is given to verify the developed approach and to demonstrate its practicality and effectiveness.