Abstract
For aggregating observed unordered n values, based on an n-ary aggregation function A, two extremal symmetric aggregation functions A* and A(*) are introduced and discussed. In the case of weighted arithmetic means, the representation of A* and A(*) as particular OWA operators is shown. Considering weighted aggregation function A(w) with unordered weights and input values to be aggregated, another two symmetric aggregation functions (A(w))(lozenge) and (A(w))(lozenge) are introduced and discussed. A relation between our approach and the Hungarian algorithm known from the linear optimization domain is also shown.