A Fractional q-Rung Orthopair Fuzzy Tensor Framework for Dynamic Group Decision-Making: Application to Smart City Renewable Energy Planning

In complex decision-making scenarios, such as smart city renewable energy project selection, decision-makers must contend with multi-dimensional uncertainty, conflicting expert opinions, and evolving temporal dynamics. This study introduces a novel Fractional q-Rung Orthopair Fuzzy Tensor (Fq-ROFT)-based group decision-making methodology that integrates the flexibility of q-rung orthopair fuzzy sets with tensorial representation and fractional-order dynamics. The proposed framework allows for the modeling of positive and negative membership degrees in a multi-dimensional, time-dependent structure while capturing memory effects inherent in expert evaluations. A detailed case study involving six renewable energy alternatives and six criteria demonstrates the method’s ability to aggregate expert opinions, compute fractional dynamic scores, and provide robust, reliable rankings. Comparative analysis with existing approaches, including classical q-ROFSs, intuitionistic fuzzy sets, and weighted sum methods, highlights the superior discriminative power, consistency, and dynamic sensitivity of the Fq-ROFT approach. Sensitivity analysis confirms the robustness of the top-ranked alternatives under variations in expert weights and fractional orders and membership perturbations. The study concludes by discussing the advantages, limitations, and future research directions of the proposed methodology, establishing Fq-ROFT as a powerful tool for dynamic, high-dimensional, and uncertain group decision-making applications.