Entropy-Based Fuzzy Data Analytics for Time-Sequential Decision Making: A Case Study in Supply Chain Optimisation

Decision-making problems in complex environments are often characterised by uncertainty, vagueness, and dynamically evolving information. In such contexts, decision makers may express hesitant and fluctuating evaluations over time, which cannot be adequately captured by classical hesitant fuzzy frameworks. To address this limitation, time-sequential hesitant fuzzy sets (TSHFSs) have been introduced as an effective tool for modelling temporal hesitancy. However, the development of information measures for TSHFSs, particularly entropy measures for quantifying uncertainty and deriving criteria weights, remains limited. In this paper, we propose a novel class of entropy measures for TSHFSs by constructing transformation mechanisms based on proximity-driven formulations derived from similarity structures. The proposed measures are developed using arithmetic and algebraic operators to capture the dispersion of information across time sequences, enabling a more refined representation of temporal uncertainty. These entropy measures are further integrated into a multi-criteria decision-making (MCDM) framework, where they are employed to determine criteria weights under incomplete information and combined with the TOPSIS method for ranking alternatives. The effectiveness of the proposed framework is validated through comparative analysis with existing TSHFS entropy measures and sensitivity analysis under varying decision conditions. The results demonstrate that the proposed measures maintain ranking consistency while providing improved discrimination and interpretability of alternatives. In particular, the framework effectively captures fluctuating hesitancy and enhances the robustness of decision outcomes in dynamic environments. The proposed approach contributes to the advancement of TSHFS-based decision analysis by offering a mathematically grounded and practically applicable entropy-driven framework for handling time-dependent uncertainty in complex decision-making problems.