This study introduces and explores the concepts of a neutrosophic \(\mathcal {N}\) -subhoop and the level set of a neutrosophic \(\mathscr {N}\) -structure defined on hoops, demonstrating their significance in analyzing neutrosophic logic within this algebraic framework. The research establishes a fundamental connection between subhoops and level sets, proving that the level set of a neutrosophic \(\mathcal {N}\) -subhoop on a hoop is itself a subhoop, and conversely. This reveals a deep interplay between these two notions. Furthermore, the study shows that the collection of all neutrosophic \(\mathcal {N}\) -subhoops of a given hoop forms a complete distributive lattice, indicating a structured and ordered hierarchy among these subhoops. Additionally, the work defines a neutrosophic \(\mathcal {N}\) -filter on hoops, investigates its properties, and demonstrates that while every neutrosophic \(\mathcal {N}\) -filter is also a neutrosophic \(\mathcal {N}\) -subhoop, the reverse does not generally hold. This distinction underscores the unique behavior and characteristics of neutrosophic \(\mathcal {N}\) -filters in this algebraic setting.
