<p>Renewable energy sources are crucial not only because traditional resources are limited but also due to their role in reducing greenhouse gas emissions and air pollution. The choice of appropriate renewable energy sources has a significant impact on both economic growth and environmental development. To address this issue, numerous researchers have focused on selecting the most appropriate renewable energy source using decision-making techniques under various fuzzy sets. Therefore, in this paper, we introduce a new multi-criteria decision-making method under the Fermatean fuzzy numbers environment to select the optimal renewable energy source for rural electrification. For this, we propose the Fermatean fuzzy Schweizer-Sklar power-weighted geometric aggregation operator based on Schweizer-Sklar’s norm. We also introduce a few desired characteristics of the proposed operator. Moreover, we develop a novel multi-criteria decision-making method under the Fermatean fuzzy environment by integrating the concept of the proposed operator and classical “evaluation based on distance from average solution” (EDAS) technique. After that, we consider a mathematical case study of the optimal renewable energy source selection for rural electrification to demonstrate the practical applicability of the proposed multi-criteria decision-making method. In this case study, we select the optimal renewable energy source from the five renewable energy sources: wind energy, biomass energy, hydropower, solar power and geothermal energy based on four criteria: environmental impact, cost, resource availability, and carbon reduction. The proposed decision making method identifies hydropower as the optimal renewable energy source for rural electrification for this mathematical case study. Finally, we present a comparative analysis of the proposed multi-criteria decision-making method with existing decision making methods to show the advantages of the proposed method.</p>