Abstract
The convex integral introduced by Mesiar et al. (Superdecomposition integrals, Fuzzy Sets Syst. 259 (2015) 3–11) is a special superdecomposition integral related to convex functional. It can be regarded as the counterpart of concave integral, but it is not fully dual to the concave integral. This paper investigates some properties of the convex integral in detail. We show which of these results are valid both for the concave and convex integrals, which are dual to each other, and which are valid only for one of these two integrals. We also provide a necessary and sufficient condition for which two concave integrals (resp. convex integral) based on different monotone measures coincide with each other.
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