MCGDM approach based on (p, q, r)-spherical fuzzy Frank aggregation operators: applications in the categorization of renewable energy sources

The growing demand for energy, driven by population growth and technological advancements, has made ensuring a sufficient and sustainable energy supply a critical challenge for humanity. Renewable energy sources, such as biomass, solar, wind, and hydro, are inexhaustible and environmentally friendly, offering a viable solution to both the energy crisis and the fight against global warming. However, selecting the optimal renewable energy source remains a complex decision-making problem due to the varying characteristics and impacts of these sources. Motivated by the need for more accurate and nuanced decision-making tools in this domain, this paper introduces a novel multicriteria group decision-making (MCGDM) approach based on \(\:(p,q,r)-\) spherical fuzzy Frank aggregation operators. By integrating Frank t-norm with \(\:(p,q,r)-\) spherical fuzzy sets, we develop aggregation operators (AOs) that effectively manage membership, neutral, and non-membership degrees through parameters \(\:p\) , \(\:q\) , and \(\:r\) . These AOs provide a more refined framework for decision-making, leading to improved outcomes. We apply this approach to evaluate and identify the superior and optimal renewable energy source using artificial data, demonstrating the advantages of the proposed operators compared to existing methods. This work contributes to the field by offering a robust tool for addressing the energy crisis and advancing sustainable energy solutions.