Type-2 triangular norms and their residual operators

In this paper, we mainly investigate T-extension operations of any t-norms and t-conorms on type-2 fuzzy sets' truth values F 2 (a set of all functions defined from 0 , 1 ] into itself). Based on it, we first construct some type-2 t-norms on the fuzzy truth values F 2 with the ordinary partial order ≤ and the partial order ? , respectively. The algebraic properties of these type-2 t-norms are then studied. Moreover, the residual operators of some special type-2 t-norms on ( F 2 , ≤ ) and ( F 2 , ? ) are respectively represented. Finally, we briefly discuss the compositional rule of inference based on type-2 t-norms and their residual operators.