ABSTRACT Renewable energy sources, such as solar, wind, and hydropower, are critical for sustainable development, environmental protection, and long‐term energy security. Selecting the most suitable renewable energy sources involves complex multi‐criteria decision‐making, considering economic, environmental, techn ological, and reliability aspects. This paper introduces a bipolar ‐fractional fuzzy set model along with corresponding aggregation operators for multi‐criteria decision‐making under uncertainty. The proposed bipolar ‐fractional fuzzy sets combine the flexibility of ‐fractional fuzzy sets with the dual‐perspective capability of bipolar fuzzy sets, enabling simultaneous representation of positive and negative evaluations. To aggregate bipolar ‐fractional fuzzy information across multiple criteria, two operators are defined: the bipolar ‐fractional fuzzy weighted average and the bipolar ‐fractional fuzzy weighted geometric operators. Their key properties, including idempotency, monotonicity, and boundedness, are also established. A systematic decision‐making algorithm is proposed, integrating these operators with score and accuracy functions to rank alternatives effectively. A practical example on renewable energy sources selection demonstrates the model's ability to preserve ranking consistency, maintain smooth score trends, and provide interpretable results. Comparative and sensitivity analyses further illustrate the robustness of the proposed approach.
Musa et al. (Wed,) studied this question.
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