The history of triangular norms started with the paper "Statistical
metrics" [Menger 1942]. The main idea of Karl Menger was to construct
metric spaces where probability distributions rather than numbers are
used in order to de- scribe the distance between two elements of the
space in question. Triangular norms (t-norms for short) naturally came
into the picture in the course of the generalization of the classical
triangle inequality to this more general set- ting. The original set of
axioms for t-norms was considerably weaker, including among others also
the functions which are known today as triangular conorms. Consequently,
the first field where t-norms played a major role was the theory of
probabilistic metric spaces ( as statistical metric spaces were called
after 1964). Berthold Schweizer and Abe Sklar in [Schweizer & Sklar
1958, 1960, 1961] provided the axioms oft-norms, as they are used
today, and a redefinition of statistical metric spaces given in
[Serstnev 1962]led to a rapid development of the field. Many results
concerning t-norms were obtained in the course of this development, most
of which are summarized in the monograph [Schweizer & Sklar 1983].
Mathematically speaking, the theory of (continuous) t-norms has two
rather independent roots, namely, the field of (specific) functional
equations and the theory of (special topological) semigroups.
