TitleA note on the duality between continuous t-norm and t-conorm operators
Publication TypeConference Paper
Year of Publication2003
AuthorsGodo L, Sandri S
Conference NameProceedings of 12th IEEE International Conference on Fuzzy Systems(FUZZ-IEEE 2003) May, 2003. St. louis

De Morgan duality between a t-norm T and a t-conorm S is defined with respect to an involutive (or strong) negation N, so that S (x, y)=N (T (N (x), N (y))), and vice versa T (x, y)=N (S (N (x), N (y))). A weaker form of duality can be met when the negation operator N is only required to be a decreasing bijection such that S=N^-1 T (N*N). In the paper we address some issues about the (general) duality between continuous t-norms and t-conorms. Given such a t-norm T and such a t-conorm S, we show how to construct a negation N (possibly non-involutive) that makes T and S become N-dual.