International Journal of Neutrosophic Science IJNS 2690-6805 2692-6148 10.54216/IJNS https://www.americaspg.com/journals/show/3813 2020 2020 Department of Mathematics, Faculty of Science, Ajloun National University, P.O. Box 43, Ajloun 26810, Jordan Anas Anas Department of Mathematics, College of Science, Qassim University, Buraydah, Saudi Arabia Fawziah Alharthi Department of Mathematics, Faculty of Science, Ajloun National University, P.O. Box 43, Ajloun 26810, Jordan Noor Bani Abd Al Al-Rahman Recent years have witnessed remarkable developments in fuzzy logic, with interval-valued fuzziness and negative structures emerging as powerful tools for modeling inaccurate phenomena. The crossing cubic structures (CCs), as a generalization of the bipolar fuzziness structures, represent a comprehensive mathematical framework capable of dealing with a wide range of fuzziness and contradictory data, thus expanding research prospects in this area. This paper has made a new contribution to some algebraic structures by investigating the concept of CCs on algebraic substructures in a hoop algebra. The concepts of crossing cubic sub-hoops (CC − SHs) and crossing cubic filters (CCFs) are introduced, and a deeper understanding is sought to analyze their characteristics. The effect on the relationship between CC − SHs and CCFs is revealed, and the characterizations of CC − SHs and CCFs are analyzed. 2025 2025 302 313 10.54216/IJNS.260322 https://www.americaspg.com/articleinfo/21/show/3813