Aggregation of indistinguishability operators

Abstract

The paper studies the aggregation of pairs of T-indistinguishability operators. More concretely we address the question whether A(E,E′) is a T-indistinguishability operator if E,E′ are T-indistinguishability operators. The answer depends on the aggregation function, the t-norm T, and the chosen T-indistinguishability operators. It is well-known that an aggregation function preserves T-transitive relations if and only if it dominates the t-norm T. We show the important role of the minimum t-norm TM in this preservation problem. In particular we develop weaker forms of domination that are used to provide characterizations of TM-indistinguishability preservation under aggregation. We also prove that the existence of a single strictly monotone aggregation that satisfies the indistinguishability operator preservation property guarantees all aggregations to have the same preservation property.