Invariant continuous aggregation functions
Continuous aggregation functions, being invariant under any monotone bijective transformation, are discussed and characterised. As a basic tool for this characterisation, self-dual {0;1}-valued capacities or their counterparts, self-dual monotone Boolean functions, are exploited. A generating role of med(x, y, z) is discussed. The relevant role of simple medians in describing monotone threshold Boolean functions is made apparent.
aggregation function capacity choquet integral invariant aggregation function self-dual capacity