BL-algebra; fuzzy logic; t-norm; t-conorm

The unified representation of continuous t-norms and t-conorms with the help of generalized additive generators has been suggested. This representation shows similar origin of triangular operations (t-norms and t-conorms) as truncated sums of negative and positive reals, respectively. Moreover, a generalized additive generator establishes an isomorphic mapping between a standard BL-algebra on [0,1] and a certain algebra of negative reals with truncated operations.

The unified representation of continuous t-norms and t-conorms with the help of generalized additive generators has been suggested. This representation shows similar origin of triangular operations (t-norms and t-conorms) as truncated sums of negative and positive reals, respectively. Moreover, a generalized additive generator establishes an isomorphic mapping between a standard BL-algebra on [0,1] and a certain algebra of negative reals with truncated operations.