Effective multi-attribute group decision-making approach to study astronomy in the probabilistic linguistic -rung orthopair fuzzy VIKOR framework.

This study employs a novel fuzzy logic-based framework to address multi-attribute group decision-making problems commonly encountered in modern astronomy. Our approach utilizes the probabilistic linguistic -rung orthopair fuzzy set (PL-ROFS) to handle the inherent uncertainties associated with astronomical data. The PL-ROFS offers significant advantages over existing fuzzy sets like probabilistic hesitant, linguistic intuitionistic, and linguistic Pythagorean fuzzy sets, which comprise both stochastic and non-stochastic uncertainties simultaneously. To aggregate the probabilistic linguistic decision information effectively, we propose two novel operators: the PL-ROF weighted power average (PL-ROFWPA) and the PL-ROF weighted power geometric (PL-ROFWPG). These operators form the foundation of a novel method within the PL-ROF environment. Furthermore, this study integrates the PL-ROF framework with the VIseKriterijumska Optimizacija I Kompromisno Resenje (VIKOR) model, a widely used decision-making (DM) tool known for its ability to balance group utility maximization with individual regret minimization. This integration leads to the PL-ROF-VIKOR model, a novel approach for ranking alternative solutions based on the subjective preferences of decision-makers. The effectiveness of the proposed method is demonstrated through a real-world case study in astronomy, accompanied by both parameter and comparative analyses. These analyses highlight the efficiency and accuracy of the PL-ROF-VIKOR model, ultimately leading to the conclusion that cosmology is the most optimal key finding in this case study.