International Journal of Neutrosophic Science IJNS 2690-6805 2692-6148 10.54216/IJNS https://www.americaspg.com/journals/show/4095 2020 2020 Umm Al-Qura University, Department of Mathematics, Mekkah, Saudia Arabia Santhakumar Santhakumar Department of Mathematics, Amrita School of Physical Sciences, Coimbatore, Amrita Vishwa Vidyapeetham, India Santhakumar. S. Department of Mathematics, Amrita School of Physical Sciences, Coimbatore, Amrita Vishwa Vidyapeetham, India Sumathi I.. R. A multi-neutrosophic set is a collection in which each element has a vector of truth indeterminacy, and falsity membership degree, rather than a Neutrosophic set. These vectors may correspond to multiple criteria, perspectives, or layers of information. Multi-neutrosophic sets are a more adaptive strategy for handling ambiguity in complex systems because they broaden neutrosophic sets and allow for better modeling of uncertain information. In this study, we have proposed the fundamental structure of multi-neutrosophic BCIBCK Algebra and extended it to the category of multi-neutrosophic BCI(BCK) algebras. Theoretical results are presented along with examples. This study advances algebraic structure to multi-neutrosophic set and provides novel directions for future research in non-classical logic. 2026 2026 392 406 10.54216/IJNS.270232 https://www.americaspg.com/articleinfo/21/show/4095