Neutrosophic theory alleviates the ambiguity situation more effectively than fuzzy sets. Neutrosophic soft set deals with the combination of truth, indeterminacy and falsity membership. This provides a space for the convention with multi-aspect decision-making (MADM) problems that involve these combinations. The main aim of this paper is to provide a unique ranking for the alternatives to overcome the existing drawbacks in the said environment. Initially, a new score function and the weighted neutrosophic vector are discussed. Secondly, to show the supremacy of the proposed score function a comparison analysis is discussed between the existing score method and the proposed approach. Thirdly, algorithm and flowchart are discussed for the case study. Lastly, a new technique for ranking the alternatives is discussed which enables us to determine the unique highest score. The working model is illustrated with suitable examples to authenticate the tool and to demonstrate the effectiveness of the planned approach. Keywords: Single valued neutrosophic sets, Neutrosophic soft matrix (NSM), weighted neutrosophic vector, Score and value function, Multi-aspect decision-analysis.