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 in [5].