•  
  •  
 

Abstract

The increasing complexity of decision-making environments demands mathematical frameworks capable of modeling bipolar, indeterminate, and phase-dependent uncertainty simultaneously. Bipolar Complex Neutrosophic theory provides such a structure, but the extension of similarity measures to matrix-based environments remains largely unexplored. In this study, we formally develop cosine, Dice, Jaccard, and hybrid vector similarity measures for Bipolar Complex Neutrosophic Matrices (BCNMs). Each matrix element is represented by a Bipolar Complex Neutrosophic Number (BCNN), enabling structured representation of multidimensional uncertainty within a matrix framework. We also design and implement efficient Python-based computational tools to automate similarity evaluation for BCNMs. The proposed algorithms reduce computational complexity, eliminate manual calculation errors, and provide scalable solutions for large datasets. The framework is illustrated through an application aligned with the United Nations Sustainable Development Goal 17 (Partnerships for the Goals), demonstrating how BCNM-based similarity analysis can support structured assessment of collaborative indicators. The proposed methodology generalizes similarity measures from Bipolar Complex Neutrosophic Sets to matrix structures, enhancing discrimination capability, structural consistency, and computational feasibility. This work contributes mathematically and practically, through both formal matrix-level similarity extensions and reproducible computational tools suitable for advanced decision-support systems.

Download

Share

COinS