Powers with respect to t-norms and t-conorms and Aggregation Functions

Abstract

Aggregation functions A stable with respect to powers of t-norms and t-conorms (i.e.: satisfying A(x^{(r)},y^{(r)})=(A(x,y))^{(r)}) where x^{(r)} is the r-th power of x \in [0,1] with respect to a t-norm or t-conorm) are characterized. This result generalizes the characterization of power stable aggregation functions.