Improving the effectiveness of green supply chains is a critical step towards minimizing waste, optimizing resource use, and reducing the environmental impact of business operations. Sustainable practices should be implemented throughout the entire supply chain, from product design and procurement to production and transportation, in order to achieve these goals. By doing so, businesses can not only improve their environmental performance but also reduce costs, increase customer satisfaction, and gain a competitive advantage in the market. However, due to the existence of competing characteristics, imprecise information, and a lack of knowledge, selecting the appropriate green provider is a complex and unpredictable decision-making issue. The primary objective of a linear-diophantine fuzzy (LiDF) framework is to assist decision makers in selecting the optimal course of action. This paper introduces several novel aggregation operators (AOs), namely the linear Diophantine fuzzy soft-max average (LiDFSMA) and the linear Diophantine fuzzy soft-max geometric (LiDFSMG) operators. The proposed method is then demonstrated through a simple example of a green supplier optimization technique containing linear Diophantine fuzzy content, showing the utility and applicability of the approach. Overall, the proposed LiDF framework and AOs can aid decision makers in selecting the most suitable green provider, thereby enhancing the efficiency of green supply chains.

The attention of many researchers has been drawn to Pythagorean fuzzy information, which involves Pythagorean fuzzy numbers and their aggregation operators. In this study, the concept of the Pythagorean fuzzy set is discussed, along with the Hamacher t-norm and t-conorm operators. Furthermore, novel aggregation operators are developed using the operational rules of the Hamacher t-norm and t-conorm. The primary objective of this article is to develop a multi-attribute decision-making method in a Pythagorean fuzzy environment using Pythagorean fuzzy Hamacher aggregation operators. It is noted that the Hamacher operator, which is a generalization of the algebraic Einstein operator and contains a parameter, is more potent than some existing operators. Finally, an example of an enterprise application software selection problem is presented to demonstrate the proposed method.

This study aimed to address the optimization of magnetically coupled resonant wireless power transfer. An equivalent circuit for the wireless power transfer was established and the factors affecting the transmission efficiency were analyzed. To optimize the system, an improved whale optimization algorithm (WOA) was proposed and applied to optimize the optimal matching values of resonant frequency and load resistance. Performance of the improved WOA was tested using different test functions, and the optimized parameters were applied to the transmission efficiency test of the wireless power transfer system. Experiments demonstrated that the improved WOA effectively optimized the transmission efficiency and achieved good application results in the intelligent transfer system.