Triangular Norms

The exploration of triangular norms originated from Karl Menger's work on statistical metrics, where probability distributions define distances in metric spaces. This concept led to the development of t-norms, which generalize the classical triangle inequality. Initially, the axioms for t-norms were less stringent, encompassing triangular conorms. Key contributions by Berthold Schweizer and Abe Sklar established the modern axioms for t-norms, facilitating advancements in probabilistic metric spaces and resulting in significant mathematical findings in functional equations and semigroup theory.