The q-rung orthopair fuzzy (q-ROF) set is an efficient tool for dealing with uncertain and inaccurate data in real-world multi-attribute decision-making (MADM). In MADM, aggregation operators play a significant role. The majority of well-known aggregation operators are formed using algebraic, Einstein, Hamacher, Frank, and Yager t-conorms and t-norms. These existing t-conorms and t-norms are some special cases of Archimedean t-conorms (ATCNs) and Archimedean t-norms (ATNs). Therefore, this article aims to extend the ATCN and ATN operations under the q-ROF environment. In this paper, firstly, we present some new operations for q-ROF sets based on ATCN and ATN. After that, we explore a few desirable characteristics of the suggested operational laws. Then, using these operational laws, we develop q-ROF Archimedean weighted averaging (geometric) operators, q-ROF Archimedean order weighted averaging (geometric) operators, and q-ROF Archimedean hybrid averaging (geometric) operators. Next, we develop a model based on the proposed aggregation operators to handle MADM issues. Finally, we elaborate on a numerical problem about site selection for software operating units to highlight the adaptability and dependability of the developed model.

Selecting sustainable suppliers in the automotive industry is crucial for fostering environmental responsibility, cost efficiency, and ethical sourcing, all of which enhance long-term competitiveness and compliance with global sustainability standards. However, this process is a complex decision-making problem due to vague, uncertain, and imprecise data stemming from subjective expert judgments, incomplete information, dynamic market conditions, evolving regulations, and diverse stakeholder expectations. Traditional methods often fail to adequately capture these intricacies, necessitating more flexible and intelligent evaluation frameworks. To address this challenge, this study leverages p,q-quasirung orthopair fuzzy sets (p,q-QOFSs) to effectively model hesitation and ambiguity in expert assessments, while incorporating confidence levels to enhance reliability by accounting for varying decision-maker expertise. We propose confidence level-based Dombi weighted averaging (geometric) aggregation operators for p,q-QOFSs and develop a multi-criteria group decision-making model, with attribute weights determined using the Analytic Hierarchy Process (AHP). The model is validated through a case study in which three experts evaluate five automotive suppliers across eight sustainability criteria. A comparative analysis with existing methods demonstrates the superiority of the proposed approach, while sensitivity analysis confirms its robustness and stability under parameter variations.