Complex Fractional Fuzzy Tensors: A Unified Framework for Multidimensional Uncertainty Modeling and Decision-Making

Uncertainty, hesitation, and multidimensional interactions are inherent in real-world decision-making. Existing fuzzy models often lack the expressiveness to simultaneously capture complex-valued uncertainty, fractional memory effects, and tensor-based multi-way relationships. To bridge this gap, this paper introduces the Complex Fractional Fuzzy Tensor (CFFT), a unified mathematical framework that integrates fractional calculus, tensor algebra, and complex-valued fuzzy logic into a single higher-order structure. The proposed model not only generalizes classical fuzzy extensions but also embeds temporal memory and phase-sensitive hesitation within a multidimensional tensor representation. A comprehensive set of CFFT operations and properties is formally defined and illustrated with examples. A novel group decision-making algorithm (CFFT-GDM) is developed and applied to a renewable energy investment case study, demonstrating its ability to aggregate hesitant expert opinions under memory-aware dynamics. Comparative statistical analysis indicates that the proposed framework achieves approximately a 12.5% improvement in modeling expressiveness, measured through a composite index combining correlation with expert consensus and stability under parameter perturbations. The framework is particularly suited for high-dimensional decision environments such as healthcare diagnostics, financial risk assessment, and sustainable energy planning. Future research directions include efficient tensor decomposition algorithms, GPU-accelerated implementations, and hybridization with deep learning architectures for scalable and adaptive decision support.