Neutrosophic Vague Hypersoft Sets on Correlation Coefficient

Abstract

Neutrosophic Vague Hypersoft Sets (NVHSSs) provide a powerful mathematical framework for representing uncertain, vague, inconsistent, and multi-attribute information encountered in complex decision-making problems. In this paper, we introduce the concept of the correlation coefficient for Neutrosophic Vague Hypersoft Sets to measure the degree of association between two NVHSSs. The proposed correlation coefficient is formulated by incorporating the truth-membership, indeterminacy-membership, and falsity-membership functions while preserving the multi-parameter structure of hypersoft sets. Fundamental properties of the proposed measure, including boundedness, symmetry, non-negativity, and identity, are established and rigorously proved. Furthermore, illustrative numerical examples are presented to demonstrate the validity and effectiveness of the proposed correlation coefficient. The proposed approach provides a reliable tool for measuring similarity and dependence under neutrosophic vague hypersoft environments and can be applied to pattern recognition, medical diagnosis, decision-making, and other uncertainty-based applications. The results indicate that the proposed correlation coefficient effectively captures the relationships between Neutrosophic Vague Hypersoft Sets and extends existing correlation measures available in the literature.