A robust fractional fuzzy decision support framework for sustainable energy planning.

The increasing global population and rapid technological advancements are driving a surge in energy demand. Meanwhile, fossil fuel dependence as a primary energy source is contributing to environmental issues, including greenhouse gas emissions and climate change. These challenges underscore the urgent necessity of transitioning to sustainable energy solutions. Renewable energy systems (RES) are critical alternatives that can facilitate sustainable development goals. Nevertheless, the selection of the most suitable RES for specific geography, particularly within Industry 4.0, poses substantial decision-making complexities due to the intricate criteria involved. This paper introduces a robust method for evaluating RES. The proposed approach integrates f, g, h-fractional fuzzy sets (f, g, h-FrFS) into multi-criteria decision-making (MCDM), enhancing the decision-making process. The f, g, h-FrFS framework effectively captures decision-makers' preferences by considering membership degrees (MB), non-membership degrees (NMB), and indeterminacy degrees (ID). Initially, the importance of evaluation criteria is determined through the improved Criteria Importance through Inter-Criteria Correlation (CRITIC) method. Following this, the WASPAS model is used to provide an accurate ranking of the RES. Geothermal energy is recognized as the most reliable RES option. To test the robustness of the proposed approach, a sensitivity analysis is conducted, demonstrating the stability of the model under varying conditions. The effectiveness of this framework is further validated through a comparative study analysis. Ultimately, this technique offers significant value for policymakers, energy managers, and organizations involved in renewable energy systems. In Industry 4.0, energy planning and development is complicated, so this tool can assist them in navigating the complexities.