A Conceptual Approach for Algebraic Structure of
Multi-Neutrosophic BCI/BCK Algebras
Omaima Al-Shanqiti1, Santhakumar S.2,∗, Sumathi I. R.2
1Umm Al-Qura University, Department of Mathematics, Mekkah, Saudia Arabia
2Department of Mathematics, Amrita School of Physical Sciences, Coimbatore,
Amrita Vishwa Vidyapeetham, India
Emails: omshanqiti@uqu.edu.sa; s santhakumar@cb.amrita.edu; ir sumathi@cb.amrita.edu
Abstract
A multi-neutrosophic set is a collection in which each element has a vector of truth indeterminacy, and fal-
sity 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
BCI/BCK 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.
Keywords: Neutrosophic set; multi-neutrosophic set; multi-neutrosophic BCI/BCK algebra; Category of
multi-neutrosophic BCI/BCK algebra