Assessment of Hydropower Plants in Pakistan: Muirhead Mean-Based 2-Tuple Linguistic T-spherical Fuzzy Model Combining SWARA with COPRAS

In the study of group decision-making, the most important issue is how to coordinate opinions from different decision experts (DEs) to reach a consensus under uncertainty. To tackle uncertainties surrounding multi-attribute group decision-making (MAGDM) problems in real-life scenes, we introduce 2-tuple linguistic T-spherical fuzzy sets (2TLT-SFSs) which generalize T-spherical fuzzy sets by means of 2-tuple linguistic terms. The 2TLT-SFS model enables the degrees of membership, abstention, and non-membership to be expressed by linguistic terms. This makes it more flexible and descriptive to model the attitudes of DEs in MAGDM applications. Due to the fact that multi-input arguments are interconnected and DEs have a lot of options perception, we also define Muirhead mean (MM) aggregation operators (AOs) to facilitate the fusion of 2TLT-SF information. With the aid of 2TLT-SFSs and MM AOs, the main goal of this research is to present a general MAGDM framework by integrating the step-wise weight assessment ratio analysis (SWARA) with the complex proportional assessment (COPRAS). Firstly, the MM, weighted MM, dual MM, and weighted dual MM operators are adapted to the 2TLT-SF environment, which put forward several new notions such as the 2-tuple linguistic T-spherical fuzzy Muirhead mean (2TLT-SFMM), 2-tuple linguistic T-spherical fuzzy weighted Muirhead mean (2TLT-SFWMM), 2-tuple linguistic T-spherical fuzzy dual Muirhead mean (2TLT-SFDMM), and 2-tuple linguistic T-spherical fuzzy weighted dual Muirhead mean (2TLT-SFWDMM) operators. Meanwhile, some properties regarding idempotency, monotonicity, boundedness, and specializations of the proposed operators are analyzed. Secondly, an integrated 2TLT-SF-MAGDM framework is established. In the proposed decision framework, the 2TLT-SF-SWARA method is utilized to identify the subjective weights of decision attributes, and the 2TLT-SF-COPRAS approach is used to rank alternatives. Lastly, a case study concerning hydropower plants assessment is presented to demonstrate that the suggested scheme is feasible and effective. Furthermore, sensitivity and comparison analyses are conducted to show the robustness and superiority of the proposed method.