Triangular Norms, Triangular Conorms, and Some Related Concepts

Abstract

Abstract. Mathematically considered, a Triangular Norm is a kind of binary operation frequently used in the context of Probabilistic Metric Spaces, but also in other very interesting fields, as may be Fuzzy Logic, or in general, in Multi-Valued Logic (MVL). The T-conorm, or S-norm, is a dual concept. Both ideas allow us to generalize the intersection and the union in a Lattice, or disjunction and conjunction in Logic. Also may be very interesting to introduce a special class of real monotone operations. We refer to the so-called Copulas, very useful in many fields. So, we offer now a comprehensive analysis of all these aggregation operators.