As a generalization of several fuzzy tools, picture fuzzy sets (PFSs) hold a special ability to perfectly portray inherent uncertain and vague decision preferences. The intention of this paper is to present a Pearson’s picture fuzzy correlation-based model for multi-attribute decision-making (MADM) analysis. To this end, we develop a new correlation coefficient for picture fuzzy sets, based on which a Pearson’s picture fuzzy closeness index is introduced to simultaneously calculate the relative proximity to the positive ideal point and the relative distance from the negative ideal point. On the basis of the presented concepts, a Pearson’s correlation-based model is further presented to address picture fuzzy MADM problems. Finally, an illustrative example is provided to examine the usefulness and feasibility of the proposed methodology.

In this paper, we consider multiple attribute group decision making (MAGDM) problems in which the attribute values take the form of intuitionistic uncertain linguistic variables. Based on Hamacher operations, we developed several Hamacher aggregation operators, which generalize the arithmetic aggregation operators and geometric aggregation operators, and extend the algebraic aggregation operators and Einstein aggregation operators. A number of special cases for the two operators with respect to the parameters are discussed in detail. Also, we developed an intuitionistic uncertain linguistic generalized Hamacher hybrid weighted average operator to reflect the importance degrees of both the given intuitionistic uncertain linguistic variables and their ordered positions. Based on the generalized Hamacher aggregation operator, we propose a method for MAGDM for intuitionistic uncertain linguistic sets. Finally, a numerical example and comparative analysis with related decision making methods are provided to illustrate the practicality and feasibility of the proposed method.

To meet the dual-carbon objective, China's economy needs to move from a carbon-intensive to a green economy. Green technology innovation and renewable energy development are key to promoting green economic growth. The study uses 2010–2022 provincial panel data from 30 Chinese provinces. The super-efficient SBM model measures the province's green economic growth index. A panel fixed-effects model is used to experimentally evaluate how green technology innovation and renewable energy development affect green economic growth. Green financing moderates and a panel threshold model tests the threshold effect of renewable energy development on green economic growth. The results demonstrate that (1) China's green economic growth is rising and has a "U" shape. (2) all selected variables significantly impact green economic growth. However, population density, government intervention, and industrial structure are inversely associated with GEG. Green economic growth is significantly boosted by the moderate role of green finance in the development of renewable energy and green technological innovation. (3) Renewable energy development has a single threshold non-linear effect on green economic growth, depending on its development level and green technological innovation. Considering China's current condition and research findings, this study examines the green energy transition to promote green economic growth and high-quality economic development. Meanwhile, puts forward some important policy recommendations.