Based on a continuous triangular norm $T$, extensions of $n$-ary aggregation acting on $[0,1]$ to $n$-ary aggregation functions acting on special fuzzy quantities are proposed and discussed. Recall that a genuine property of standard aggregate functions is their increasingness in each coordinate, based on the fact that $[0,1]$ is a chain. On fuzzy quantities, some different order relations are considered and the corresponding $T$-extensions monotone with respect to them are studied. Moreover, several properties of aggregation functions for $T$-extensions are discussed, such as symmetry, associativity, bisymmetry, idempotency, neutral and absorbing elements.
Reviewer: Radko Mesiar (Bratislava)