The growing complexity of modern decision-making environments, characterized by multi-dimensional data, uncertainty, and dynamic behavior, demands advanced mathematical frameworks for effective information aggregation. Although fractional fuzzy tensor (FFT) models provide a powerful tool for representing such complex systems by integrating fuzzy logic, tensor structures, and fractional dynamics, the lack of suitable aggregation mechanisms significantly limits their practical applicability. To address this challenge, this paper proposes a novel family of Bonferroni mean-based aggregation operators within the fractional fuzzy tensor environment. The proposed framework extends the classical Bonferroni mean to multi-dimensional fractional fuzzy settings, enabling the effective modeling of interrelationships among criteria while preserving the structural and dynamic properties of FFTs. Specifically, four aggregation operators—namely, the fractional fuzzy tensor Bonferroni mean (FFT-BM), weighted Bonferroni mean (FFT-WBM), ordered Bonferroni mean (FFT-OBM), and hybrid Bonferroni mean (FFT-HBM)—are systematically developed. A comprehensive theoretical analysis is conducted to investigate fundamental properties such as idempotency, monotonicity, boundedness, commutativity, and stability, thereby establishing the mathematical consistency and reliability of the proposed operators. Furthermore, a structured multi-criteria decision-making (MCDM) algorithm is formulated, incorporating tensor construction, aggregation, evaluation, and sensitivity analysis phases to handle complex uncertain information effectively. To demonstrate the practical applicability of the proposed framework, a real-world case study related to disaster management decision-making is presented. The results are further validated through quantitative comparative analysis with classical and recent aggregation operators, revealing improved discrimination power, robustness, and ranking consistency. Additionally, sensitivity analysis confirms the stability of the proposed approach under varying parameters. The findings indicate that the proposed Bonferroni mean-based aggregation framework significantly enhances the capability of FFT models in handling high-dimensional, uncertain, and dynamic decision-making problems. This study not only strengthens the theoretical foundation of aggregation in tensor-based fuzzy environments but also provides a flexible and reliable decision-support tool for complex real-world applications.
Bilal et al. (Thu,) studied this question.