A characterization of the ordering of continuous t-norms

Abstract

Given two t-norms T1 and T2, it is quite often difficult or even impossible to check directly whether T1≤ T2. In Schweizer and Sklar (1983), a necessary and sufficient condition is given for continuous Archimedean t-norms to be comparable. We simplify this result, proving a sufficient condition which involves only one argument of a one-place function rather than two arguments. This result is applied to show the monotonicity of some well-known classes of t-norms. Next, we generalize the result of Schweizer and Sklar to the case of all continuous t-norms and present also a sufficient condition, which is again easier to check. © 1997 Elsevier Science B.V.