We investigate a relation about subadditivity of functions. Based on subadditivity of functions, we consider some conditions for continuous $t$-norms to act as the weakest $t$-norm $T_W$-based addition. This work extends some results of Marková-Stupňanová , Mesiar .
triangular norms, fuzzy arithmetics, fuzzy intervals
93E12, 62A10, 62F15