Interval-valued Pythagorean fuzzy distance-based extended inferior ratio method for multiattribute decision-making: Application to green supplier selection in manufacturing industry

Interval-valued Pythagorean fuzzy sets (IVPFSs) have emerged as a powerful tool for handling uncertainty and vagueness in multiattribute decision-making (MADM). In this paper, we first propose a novel distance measure for IVPFSs based on triangular divergence, which satisfies all core distance axioms and significantly improves discrimination ability compared to existing measures. Building on this, we introduce a maximizing deviation strategy with a new loss function to objectively determine attribute weights. Furthermore, we develop an extended inferior ratio (EIR) method that incorporates a dynamic weight parameter to flexibly balance the influence of positive and negative ideal solutions. The performance of the proposed method is demonstrated through a case study on green supplier selection in the manufacturing industry. The results indicate that, among the seven criteria evaluated, the most suitable suppliers are ranked as follows: $\beta$ (1.0000), $\alpha$ (0.6471), $\delta$ (0.3500), $ϵ$ (0.0690), and $\theta$ (0.0000). In addition, sensitivity and comparative analyses confirm the robustness and consistency of the proposed method, reflecting its effectiveness and practical value for sustainable decision-making in real-world scenarios.