An Uncertainty-Robust Decision Framework Based on Fractional Einstein Aggregation for Prioritizing Renewable Power Generation Technologies with Unknown Weights

Renewable power generation plays a central role in the transition toward sustainable, low-carbon energy systems. However, selecting an appropriate technology remains challenging because technical, economic, environmental, and operational criteria may conflict, while expert judgments may involve uncertainty and diversity. To address these challenges, this study proposes a fractional fuzzy multi-criteria group decision-making framework for evaluating and ranking renewable power generation technologies under uncertain expert assessments. A new family of aggregation operators is developed by incorporating fractional fuzzy information into the Einstein operational framework, providing a mechanism for representing and aggregating uncertain assessments. An entropy-based weighting mechanism is further employed to determine criterion weights from the available decision information. The proposed components are integrated into a unified decision procedure that combines expert weighting, fractional fuzzy aggregation, criterion weighting, and distance-based TOPSIS assessment within a common computational framework. The numerical case study considers technical, economic, environmental, and operational criteria for renewable power generation technology selection. A sensitivity analysis examines the influence of the fractional parameters on the resulting rankings, while a comparative analysis with existing decision-making approaches is conducted to examine the consistency of the obtained results. The findings demonstrate the application of the proposed framework under the specified assessment conditions and illustrate the role of fractional fuzzy information and Einstein-based aggregation in the decision process. The study provides an integrated approach for incorporating uncertain expert information into renewable energy technology selection.