An extended COPRAS method based on complex q-rung orthopair fuzzy 2-tuple linguistic Maclaurin symmetric mean aggregation operators

The complex q-rung orthopair fuzzy 2-tuple linguistic set (Cq-ROFTLS), which merges the concepts of complex q-rung orthopair fuzzy sets (Cq-ROFS) and 2-tuple linguistic terms, offers significant advantages in dealing with uncertain and imprecise information during decision-making by effectively representing two-dimensional information within a single set. Notably, the Cq-ROFTLS introduces phase terms that empower experts to express their perspectives flexibly, particularly enhancing its capacity to address periodic elements. To address uncertainty, this approach employs complex values to quantify both membership and non-membership degrees within 2-tuple linguistic environment. Additionally, this research introduces the generalized Maclaurin symmetric mean (MSM) aggregation operator, specifically designed for Cq-ROFTL information. This introduces the Cq-ROFTLMSM and its dual form, the Cq-ROFTL Dual MSM (Cq-ROFTLDMSM), each carrying valuable properties. In cases where the importance of input factors varies, the study proposes the Cq-ROFTL weighted MSM (Cq-ROFTLWMSM) and its dual form, the Cq-ROFTL weighted dual MSM (Cq-ROFTLWDMSM). These operators not only make their debut but also showcase their properties and applications. They flexibly adjust to the significance of inputs, leading to a more refined decision-making process. The methodology extends to address multi-attribute group decision-making (MAGDM) within the Cq-ROFTL framework using the Complex Proportional Assessment (COPRAS) method. The introduction of new aggregation techniques further enhances this approach. A practical illustration involving the selection of the optimal bio-energy production technology (BPT) highlights the real-world effectiveness of the methodology. Through thorough comparisons and a focused exploration of advantages, the study effectively validates the merits of this approach.