Extended triangular norms

The paper is devoted to classical t-norms extended to operations on fuzzy quantities in accordance with the generalized Zadeh extension principle. Such extended t-norms are used for calculating intersection of type-2 fuzzy sets. Analytical expressions for membership functions of some extended t-norms are derived assuming special classes of fuzzy quantities, i.e., fuzzy truth intervals or fuzzy truth numbers. The possibility of applying these results in the construction of type-2 adaptive network fuzzy inference systems is illustrated on several examples.