The notion of a quadripartitioned single-valued neutrosophic set (in short QSVNS) is considered to be the more general mathematical framework of the neutrosophic set to model indeterminacy. In QSVNS, the indeterminacy component is divided into two parts, namely, “unknown” and “contradiction”. In a real-life scenario, while handling indeterminacy, we may have some hesitation about whether the indeterminacy occurs due to the belongingness or the non-belongingness of an object. This leads to the introduction of QSVNS. On the other hand, the theory of rough set (RS) is introduced to depict the incomplete data hidden in nature with an aid of equivalence relation. So, by combining the QSVNS and the RS, a new mathematical structure known as a quadripartitioned single-valued neutrosophic rough set is formed. The main purpose of this article is to present two types of quadripartitioned single-valued neutrosophic covering rough set models. Also, we have introduced QSVN β-covering approximation space and studying some of its properties. Based on QSVN β -covering approximation spaces, two types of QSVN covering rough set models are investigated. Furthermore, a matrix representation of the QSVN covering-based rough set model is developed. Finally, an algorithm-based model under QSVN covering-based rough set is developed and employed in a case study to diagnose a patient/s that is more likely suffering from a disease having certain symptoms.
