= 1 it is the Hamacher product). The family is strictly increasing and continuous with respect to p. The Dombi t-norm for 0 < p < +∞ arises from the Hamacher product t-norm by raising its additive generator to the power of p. An additive generator of for 0 < p < +∞ is Sugeno–Weber t-norms The family of Sugeno–Weber t-norms was introduced in the early 1980s by Siegfried Weber; the dual t-conorms were defined already in the early 1970s by Michio Sugeno. It is given for −1 ≤ p ≤ +∞ by The Sugeno–Weber t-norm is nilpotent if and only if −1 < p < +∞ (for p = 0 it is the Łukasiewicz t-norm). The family is strictly increasing and continuous with respect to p. An additive generator of for 0 < p < +∞ [sic] is Ordinal sums The ordinal sum constructs a t-norm from a family of t-norms, by shrinking them into disjoint subintervals of the interval [0, 1] and completing the t-norm by using the minimum on the rest of the unit square. It is based on the following theorem: Let Ti for i in an index set I be a family of t-norms and (ai, bi) a family of pairwise disjoint (non-empty) open subintervals of [0, 1]. Then the function T: [0, 1]2 → [0, 1] defined as is a t-norm. ] The resulting t-norm is called the ordinal sum of the summands (Ti, ai, bi) for i in I, denoted by or if I is finite. Ordinal sums of t-norms enjoy the following properties: Each t-norm is a trivial ordinal sum of itself on the whole interval [0, 1]. The empty ordinal sum (for the empty index set) yields the minimum t-norm Tmin. Summands with the minimum t-norm can arbitrarily be added or omitted without changing the resulting t-norm. It can be assumed without loss of generality that the index set is countable, since the real line can only contain at most countably many disjoint subintervals. An ordinal sum of t-norm is continuous if and only if each summand is a continuous t-norm. (Analogously for left-continuity.) An ordinal sum is Archimedean if and only if it is a trivial sum of one Archimedean t-norm on the whole unit interval. An ordinal sum has zero divisors if and only if for some index i, ai = 0 and Ti has zero divisors. (Analogously for