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

Abstract

First, a characterization is given for the continuity of a class of left-continuous triangular norms: it is established that a left-continuous triangular norm with strong induced negation is continuous if and only if it is strictly increasing on the domain where its value is positive. Second, we show that axioms of a left-continuous triangular norm with strong induced negation are not independent, namely, the boundary condition follows from the other axioms.