Aggregation Operators and the Lipschitzian Condition

Lipschitzian and kernel aggregation operators with respect to the natural
T
-indistinguishability operator Et and their powers are studied. A t-norm
T
is proved to be E
_T
-Lipschitzian, and is interpreted as a fuzzy point and a fuzzy map as well. Given an Archimedean t-norm
T
with additive generator t, the quasi-arithmetic mean generated by t is proved to be the most stable aggregation operator with respect to
T
.