is the Łukasiewicz t-norm). The family is strictly decreasing for p ≥ 0 and continuous with respect to p in [−∞, +∞]. An additive generator for for −∞ < p < +∞ is Hamacher t-norms The family of Hamacher t-norms, introduced by Horst Hamacher in the late 1970s, is given by the following parametric definition for 0 ≤ p ≤ +∞: The t-norm is called the Hamacher product. Hamacher t-norms are the only t-norms which are rational functions. The Hamacher t-norm is strict if and only if p < +∞ (for p = 1 it is the product t-norm). The family is strictly decreasing and continuous with respect to p. An additive generator of for p < +∞ is Frank t-norms The family of Frank t-norms, introduced by M.J. Frank in the late 1970s, is given by the parametric definition for 0 ≤ p ≤ +∞ as follows: The Frank t-norm is strict if p < +∞. The family is strictly decreasing and continuous with respect to p. An additive generator for is Yager t-norms The family of Yager t-norms, introduced in the early 1980s by Ronald R. Yager, is given for 0 ≤ p ≤ +∞ by The Yager t-norm is nilpotent if and only if 0 < p < +∞ (for p = 1 it is the Łukasiewicz t-norm). The family is strictly increasing and continuous with respect to p. The Yager t-norm for 0 < p < +∞ arises from the Łukasiewicz t-norm by raising its additive generator to the power of p. An additive generator of for 0 < p < +∞ is Aczél–Alsina t-norms The family of Aczél–Alsina t-norms, introduced in the early 1980s by János Aczél and Claudi Alsina, is given for 0 ≤ p ≤ +∞ by The Aczél–Alsina t-norm is strict if and only if 0 < p < +∞ (for p = 1 it is the product t-norm). The family is strictly increasing and continuous with respect to p. The Aczél–Alsina t-norm for 0 < p < +∞ arises from the product t-norm by raising its additive generator to the power of p. An additive generator of for 0 < p < +∞ is Dombi t-norms The family of Dombi t-norms, introduced by József Dombi (1982), is given for 0 ≤ p ≤ +∞ by The Dombi t-norm is strict if and only if 0 < p < +∞ (for p