t-norm; t-conorm; BL-algebra; additive generator

We have suggested the representation of continuous t-norms and t-conorms with help of generalized additive generators. This representation shows similar origin of triangular operations (t-norms and t-conorms) as truncated sums of negative and positive reals, respectively. Moreover, we showed that a generalized additive generator establishes an isomorphic mapping between a standard BL-algebra on $[0,1]$ and the algebra on the set of couples of reals with truncated operations.

We have suggested the representation of continuous t-norms and t-conorms with help of generalized additive generators. This representation shows similar origin of triangular operations (t-norms and t-conorms) as truncated sums of negative and positive reals, respectively. Moreover, we showed that a generalized additive generator establishes an isomorphic mapping between a standard BL-algebra on $[0,1]$ and the algebra on the set of couples of reals with truncated operations.