Published Paper Details:

The challenge of managing uncertainty, imprecision, and indeterminacy in multi-attribute decision-making processes continues to pose difficulties in mathematical modeling. Neutrosophic Vague Sets and Hypersoft Sets each provide strong frameworks for addressing indeterminate data across multi-dimensional disjoint attribute sub-domains; however, their matrix representations currently lack a formal algebraic structure to facilitate complex logical evaluations. This study aims to fill this void by formally introducing logical operations for Neutrosophic Vague Hypersoft Matrices (NVHSMs) and systematically establishing their essential properties. The main goal of this research is to construct and investigate fundamental logical operators--namely the AND, OR, NOT, Union, and Intersection matrices--within the NVHSM framework. The approach is based on precise mathematical definitions of these operators, followed by a detailed theoretical investigation of their algebraic properties. The theoretical validity and structural coherence are actively illustrated and confirmed through sequential numerical examples. The key findings demonstrate that these proposed logical operations effectively maintain the integrity of neutrosophic vague data while precisely aggregating complex information from hypersoft attribute sets. The primary contribution of this research is the development of an accurate matrix-based computational tool that improves the processing of indeterminate information. As a result, this study has important practical implications for advanced multi-criteria decision-making (MCDM) systems. The proposed NVHSM logical operations create a foundational computational framework anticipated to enhance outcomes in intricate scenarios such as personnel selection, resource distribution, and broader management approaches, addressing the computational challenges of prior models when managing overlapping uncertainties.