BL-algebra; extensional function; disjunctive and conjunctive normal forms; Lipschitz condition

The class of functions which can be represented by formulas of a standard BL-algebra whose basic operation is a t-norm is fully characterized. We prove that the class of functions which are represented by such formulas coincides with the class of extensional functions. Moreover, the class of these functions coincides with the class of Lipschitz continuous functions in the case of BL-algebra whose t-norm has a continuous additive generator.

The class of functions which can be represented by formulas of a standard BL-algebra whose basic operation is a t-norm is fully characterized. We prove that the class of functions which are represented by such formulas coincides with the class of extensional functions. The proof is based on the uniform representation by the generalized normal (disjunctive and conjunctive) forms. Moreover, the class of these functions coincides with the class of Lipschitz continuous functions in the case of BL-algebra whose t-norm has a continuous additive generator.