Aggregation Operators and the Lipschitzian Condition

Abstract

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.