Construction of T-norms - Parametric Classes of T-norms

Parametric Classes of T-norms

Many families of related t-norms can be defined by an explicit formula depending on a parameter p. This section lists the best known parameterized families of t-norms. The following definitions will be used in the list:

• A family of t-norms T_p parameterized by p is increasing if T_p(x, y) ≤ T_q(x, y) for all x, y in whenever p ≤ q (similarly for decreasing and strictly increasing or decreasing).

• A family of t-norms T_p is continuous with respect to the parameter p if

for all values p₀ of the parameter.