In this article, we present two novel hybrid decision-making models for solving multi-criteria group decision-making (MCGDM) problems, with a focus on selecting the most suitable industrial robot. The proposed models combine the linguistic TOPSIS and linguistic GRA methods with linguistic pq-rung orthopair fuzzy sets (Lpq-ROFSs) and Hamacher aggregation operators to improve decision-making process under uncertainty. The Lpq-ROFSs extend traditional fuzzy models by introducing two parameters, \(p\) and q, which independently control membership and non-membership degrees, providing greater flexibility for handling uncertain and imprecise expert evaluations. To support this framework, we develop score and accuracy functions, a distance measure, and linguistic Hamacher aggregation operators (Lpq-ROFHWA and Lpq-ROFHWGA) for effective modeling and aggregation of expert opinions. To validate the proposed models, we applied them to a real-world problem of industrial robot selection. Data were collected from four experts in the form of linguistic pq-rung orthopair fuzzy numbers and processed through the proposed models. The results consistently identified SCARA robots as the best alternative due to their superior memory capacity, high acceleration, versatile load handling, and energy efficiency, making them an economically balanced choice. Comparative analysis with established MCGDM methods such as CODAS, WASPAS, WS, WP, BWM, MOORA, EDAS, VIKOR, and MABAC showed consistent rankings, confirming the validity and reliability of the proposed framework. Furthermore, sensitivity analysis by varying the Hamacher parameter \(\vartheta \) and the GRA parameter \(\omega \) demonstrated stable outcomes, with SCARA maintaining its top position, underscoring the robustness of the models. Overall, the proposed models provide a reliable, flexible, and efficient decision-support framework for addressing complex MCGDM problems under uncertainty, with promising applications in robotics, logistics, and other industrial domains.
