The single-valued neutrosophic set (\(\mathcal {SVNS}\)) defined to incorporate the indeterminate, imprecise, and inconsistent data in real-life scientific and engineering problems. The uncertain information is significantly measured by similarity and dissimilarity measures. The similarity and dissimilarity measures are employed to depict the closeness and differences among SVNSs and have many applications in real-life situations like medical diagnosis, data mining, decision making, classification, and pattern recognition. This paper investigates the new similarity and dissimilarity measures for the SVNS. Additional properties of the newly proposed similarity and dissimilarity measures are focused. Their corresponding weighted similarity and dissimilarity measures are discussed on. It can be seen that the newly proposed similarity and dissimilarity measures respect all the axioms of similarity and dissimilarity definitions. The notion of \(\simeq ^{\alpha }\) similar relation is defined and it can be seen that the \(\simeq ^{\alpha }\) similar relation is reflective and symmetric but not transitive. The numerical examples are provided for the explanations.