In this contribution we modify the definitions of the super-additive and sub-additive transformations of aggregation functions. Firstly, we define k-bounded transformations that represent only finite decompositions with at most k elements. Secondly, we introduce two other transformations that preserve the super-additivity property in some sense. Also, a remark on continuity of the classical super-additive transformation of an aggregation function is presented for one-dimensional case.
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