Triangular norms: Basic notions and properties

The basic definitions concerning triangular norms and conorms are collected in this chapter. We also mention the most important algebraic and analytical properties a triangular norm may have. We discuss in detail the construction of triangular norms by means of additive and multiplicative generators and via ordinal sums, and we mention also some other construction methods. Finally we present the representation theorems of continuous Archimedean triangular norms (via continuous additive or multiplicative generators) and of continuous triangular norms (as ordinal sums of continuous Archimedean triangular norms).