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As an improved form of fuzzy sets (FSs), spherical fuzzy sets (SFSs) could provide decision makers (DMs) with more free space to express their preference information. In this article, we first develop some Hamacher power aggregation operators under SFSs by power operators and Hamacher operators, including spherical fuzzy Hamacher power average (SFHPA) operator, spherical fuzzy Hamacher power geometric (SFHPG) operator, spherical fuzzy Hamacher power weighted average (SFHPWA) operator, spherical fuzzy Hamacher power weighted geometric (SFHPWG) operator, spherical fuzzy Hamacher power ordered weighted average (SFHPOWA) operator, spherical fuzzy Hamacher power ordered weighted geometric (SFHPOWG) operator, spherical fuzzy Hamacher power hybrid average (SFHPHA) operator and spherical fuzzy Hamacher power hybrid geometric (SFHPHG) operator. At the same time, some properties of the proposed operators are investigated, and the relationships between these operators and existing operators are discussed. Furthermore, a novel spherical fuzzy entropy measure is introduced to calculate unknown attribute weights. Then, some novel multiple attribute group decision making (MAGDM) methods are established by the proposed operators as well as entropy measure under SFSs. Lastly, the practicability of the presented methods is verified with a numerical case. Moreover, the robustness, availability and superiority for the developed methods are demonstrated via sensitivity analysis and further comparation with the existing methods.

Green supply chain management attaches great importance to the coordinated development of social economy and ecological environment, and requires enterprises to consider environmental protection factors in product design, packaging, procurement, production, sales, logistics, waste and recycling. Suppliers are the “source” of the entire supply chain, and the choice of green suppliers is the basis of green supply chain management, and their quality will directly affect the environmental performance of enterprises. The green supplier selection is a classical multiple attribute group decision making (MAGDM) problems. Interval-valued intuitionistic fuzzy sets (IVIFSs) are the extension of intuitionistic fuzzy sets (IFSs), and are utilized to depict the complex and changeable circumstance. To better adapt to complex environment, the purpose of this paper is to construct a new method to solve the MAGDM problems for green supplier selection. Taking the fuzzy and uncertain character of the IVIFSs and the psychological preference into consideration, the original MABAC method based on the cumulative prospect theory (CPT) is extended into IVIFSs (IVIF-CPT-MABAC) method for MAGDM issues. Meanwhile, the method to evaluate the attribute weighting vector is calculated by CRITIC method. Finally, a numerical example for green supplier selection has been given and some comparisons is used to illustrate advantages of IVIF-CPT-MABAC method and some comparison analysis and sensitivity analysis are applied to prove this new method’s effectiveness and stability.

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In recent years, the multi-attribute group decision making (MAGDM) problem has received extensive attention and research, and it plays an increasingly important role in our daily life. Fuzzy environment provides a more accurate decision-making environment for decision makers, so the research on MAGDM problem under fuzzy environment sets (SFSs) has become popular. Taxonomy method has become an effective method to solve the problem of MAGDM. It also plays an important role in solving the problem of MAGDM combined with other environments. In this paper, a new method for MAGDM is proposed by combining Taxonomy method with SFSs (SF-Taxonomy). In addition, we use entropy weight method to calculate the objective weight of attributes, so that more objective results can be produced when solving MAGDM problems.