Continuity of left-continuous triangular norms with strong induced negations and their boundary condition

First, a characterization is given for the continuity of a class of left-co ntinuous triangular norms: it is established that a left-continuous triangu lar norm with strong induced negation is continuous if and only if it is st rictly increasing on the domain where its value is positive. Second, we sho w that axioms of a left-continuous triangular norm with strong induced nega tion are not independent, namely, the boundary condition follows from the o ther axioms. (C) 2001 Elsevier Science B.V. All rights reserved.