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.

In this paper, the panel data of 19 out of 21 APEC members from 1993 to 2018 is selected as a research sample. Firstly, based on the extended Cobb-Douglas production function, the relationship between CO₂ emissions and economic growth is explored via the panel data methods, which fully consider the endogeneity between variables and the unobserved individual heterogeneity. Secondly, to examine the driving effect of CO₂ emissions on economic growth, the Empirical Likelihood for Generalized method of moments with nonparametric estimation characteristics is utilized to calculate the returns on economic scale and the corresponding confidence interval. The results show that CO₂ emissions have a significant positive impact on economic growth. Moreover, the confidence interval of returns to economic scale is very small, indicating current levels of CO₂ emissions have reached the limit to drive economic growth when the technical level, labor employment, capital, urbanization, trade, and other factors tend to stabilize. Finally, some recommendations were presented to achieve sustainable development goals.