Fuzzy clustering is widely used in business, biology, geography, coding for the internet and more. A single-valued neutrosophic set is a generalized fuzzy set, and its clustering algorithm has attracted more and more attention. An equivalence matrix is a common tool in clustering algorithms. At present, there exist no results constructing a single-valued neutrosophic number equivalence matrix using t-norm and t-conorm. First, the concept of a ( T , S ) -based composition matrix is defined in this paper, where ( T , S ) is a dual pair of triangular modules. Then, a ( T , S ) -based single-valued neutrosophic number equivalence matrix is given. A λ -cutting matrix of single-valued neutrosophic number matrix is also introduced. Moreover, their related properties are studied. Finally, an example and comparison experiment are given to illustrate the effectiveness and superiority of our proposed clustering algorithm.