– Similarity measure plays an important role in medical diagnosis. In this paper, a new rough cotangent similarity measure between two rough neutrosophic sets is proposed. The notion of rough neutrosophic set is used as vector representations in 3D-vector space. The rating of all elements in rough neutrosophic set is expressed with the upper and lower approximation operator and the pair of neutrosophic sets which are characterized by truth-membership degree, indeterminacy-membership degree, and falsitymembership degree. A numerical example of the medical diagnosis is provided to show the effectiveness and flexibility of the proposed method