Decision Analysis Using Energy of Neutrosophic Hesitant Fuzzy Soft Sets

In this paper, we introduce a novel hybrid structure called the neutrosophic hesitant fuzzy soft set (NHFSS), which integrates the flexibility of hesitant fuzzy information with the expressive capacity of neutrosophic and soft set theories. Motivated by the need to handle multiple layers of uncertainty in decision-making problems, we propose a new framework for modeling such environments. Building upon this structure, we define two complementary measures: the pessimistic energy and the optimistic energy of an NHFSS, which capture lower-bound and upperbound contributions of the hesitant and neutrosophic elements, respectively. These measures are then synthesized to derive the total energy of the NHFSS. We develop a decision-making algorithm based on this energy characterization and apply it to a real-world example to demonstrate its effectiveness. A comparative analysis is conducted to highlight the advantages of the proposed approach over existing models. Our findings suggest that the energy-based treatment of NHFSSs provides a robust and discriminative framework for multi-criteria decision-making under complex uncertainty.