Binary copulas as aggregation functions

摘要

We present binary copulas or 2-copulas (copulas, shortly) as important aggregation function. Since generally copulas are non-associative operation we restrict on binary case, which is mostly used in the practice. After giving some introductory part on general aggregation functions we restrict on specific properties of copulas. We present important applications of copulas in the theory of probabilistic metric spaces, statistics, non-additive integrals. We present invariant copulas and their application in the theory of aggregation operators.