Comparison of t-norms

Abstract

We have already seen that there is a strict (pointwise) order relationship (1.5) between the four basic t-norms T _M, T _P, T _L, and T _D, and that each t-norm lies between the two extremes T _M and T _D (see (1.4)). It is also clear that the pointwise comparison of two t-norms is a partial order. For two arbitrary t-norms, however, it may be difficult to decide whether they are comparable or not. A well-known example was the family of Frank t-norms (see Section 4.4) whose monotonicity was shown first in [Butnariu & Klement 1993].

The fundamental importance of the subject of order may be inferred from the fact that all the concepts required in geometry can be expressed in terms of the concept of order alone.

Edward V. Huntington