A CHARACTERIZATION OF THE ORDERING OF CONTINUOUS T-NORMS

Given two t-norms T-1 and T-2, it is quite often difficult or even imp ossible to check directly whether T-1 less than or equal to T-2. In Sc hweizer and Sklar (1983), a necessary and sufficient condition is give n for continuous Archimedean t-norms to be comparable. We simplify thi s result, proving a sufficient condition which involves only one argum ent 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. (C) 1997 Elsevier Science B.V.