Continuous completions of triangular norms known on a subregion of the unit interval

Abstract The continuous extensions of a t-norm know only on some subregion of the unit interval to the whole unit interval are studied. The conditions which a t-norm T 1 should satisfy on [ a , b ] 2 necessary for the existence of a continuous t-norm T 2 that coincides with T 1 on [ a , b ] 2 are given. Construction of such a continuous t-norm T 2 is described.