\input zb-basic \input zb-ioport \iteman{io-port 06112069} \itemau{Stup\v{n}anov\'a, Andrea} \itemti{A note on decomposition integrals.} \itemso{Greco, Salvatore (ed.) et al., Advances in computational intelligence. 14th international conference on information processing and management of uncertainty in knowledge-based systems, IPMU 2012, Catania, Italy, July 9--13, 2012. Proceedings, Part IV. Berlin: Springer (ISBN 978-3-642-31723-1/pbk; 978-3-642-31724-8/ebook). Communications in Computer and Information Science 300, 542-548 (2012).} \itemab Summary: Based on the idea of the decomposition integral proposed by Event and Lehrer, we introduce a new type of integrals. Moreover, we study the classes of measures turning inequalities (or incomparability) between special integrals such as Shilkret, Choquet, concave etc. integrals, into equalities. \itemrv{~} \itemcc{} \itemut{} \itemli{doi:10.1007/978-3-642-31724-8\_57} \end