Following our submission to IPMU, Aoi and I worked on this article for MDAI, which was held in Kitakyushu, Japan. In this case we were interested in how the overall function behaviour changes with respect to the different components. (available online)

**Title:** Orness and cardinality indices for averaging inclusion-exclusion integrals

**Authors:** A. Honda, S. James and S. Rajasegarar

**Abstract**

The inclusion-exclusion integral is a generalization of the discrete Choquet integral, defined with respect to a fuzzy measure and an interaction operator that replaces the minimum function in the Choquet integral’s M\”obius representation. While in general this means that the resulting operator can be non-monotone, we have previously proposed using averaging aggregation functions for the interaction component, which under certain requirements can produce non-linear, but still averaging, operators. Here we consider how the orness of the overall function changes depending on the chosen component functions and hence propose a simplified calculation for approximating the orness of an averaging inclusion-exclusion integral.