Multi-Valued Bipolar Neutrosophic Matrices: Operations and Application to Simplified-TOPSIS

This paper introduces the new concept of multi-valued bipolar neutrosophic matrix (MVBNM), which is an extension of the multi-valued neutrosophic matrix (MVNM) and simultaneously captures positive and negative membership degrees of truth, indeterminacy, and falsity, incorporating multi-valued quantities. We proposed the determinant, trace, and adjoint of the matrices and various operations, and proved basic algebraic properties through a set of propositions. In the practical application of MVBNM, the new linguistic variable corresponding to multi-valued bipolar neutrosophic numbers (MVBNNs) is introduced, and the proposed linguistic variable’s application is numerically demonstrated by using the neutrosophic simplified TOPSIS approach. Finally, an example is given to illustrate the best apartment is given to show the applicability of the proposed decision-making method. A comparative analysis with the multi-valued neutrosophic matrices (MVNMs) is also provided.