An Investigation of Circular Picture Fuzzy Muirhead Means with a Decision-Making Framework for Evaluating Renewable Energy Sources

The decision-making system plays an important role in renewable energy sources. Assessing and effectively utilizing renewable energy sources is essential to any country's sustainable strategies. However, evaluating energy sources is a tough call. To address such challenges, researchers apply decision-making processes to identify the optimal choice among multiple alternatives. This involves analyzing various options, assessing their potential outcomes, and making informed decisions based on available data and specific objectives. The goal of this article is to define a circular picture fuzzy set and its basic operations and then demonstrate them with an example, which is the advanced version of circular intuitionistic fuzzy set theory. Additionally, we proposed Muirhead mean, weighted Muirhead mean, dual Muirhead mean, and dual weighted Muirhead mean models in the framework of circular picture fuzzy set, which deals with the uncertainties and complexities in the integrated data of renewable energy sources. Further, we establish some essential properties of our proposed aggregation models, methodology, and algorithm for multi-criteria decision-making problems. The defined fuzzy aggregation models significantly handle uncertainties in hypothetical data obtained by the decision-making procedure for renewable energy sources. A sensitivity and computational analysis illustrates the effectiveness and reliability of these approaches. Finally, we adopted the comparative analysis and highlighted the advantages of defined work.