Construction of T-norms - Generators of T-norms

Generators of T-norms

The method of constructing t-norms by generators consists in using a unary function (generator) to transform some known binary function (most often, addition or multiplication) into a t-norm.

In order to allow using non-bijective generators, which do not have the inverse function, the following notion of pseudo-inverse function is employed:

Let f: → be a monotone function between two closed subintervals of extended real line. The pseudo-inverse function to f is the function f (−1): → defined as