Characterization of invariant aggregation operators

Following the ideas of Bartlomiejczyk and Drewniak, minimal invariant subsets of [0,1]n are investigated. An equivalence relation on these subsets is introduced. Consequently, invariant aggregation operators are characterized by means of Choquet integralbased representation. There are exactly 68 binary invariant aggregation operators, 4 among them are also continuous. Further, there are 6 self-dual invariant binary aggregation operators. A recurrent method of constructing invariant aggregation operators for n>2 is proposed. Restriction of invariant aggregation operators to finite scales is also discussed.