This is the first collaboration with Aoi Honda, looking at some extensions of the inclusion-exclusion integral she proposed to generalize the Choquet integral. This paper explored the conditions under which our extension satisfied monotonicity and averaging behaviour. It was presented at IFSA held in Otsu, Japan this year. (available online)
Title: Averaging Aggregation Functions Based on Inclusion-exclusion Integrals
Authors: A. Honda and S. James
The inclusion-exclusion integral, defined with respect to a fuzzy measure and interaction operator generalizes the Choquet integral. Here we look at some of its interesting properties and investigate the conditions on the interaction operator which ensure the integral is averaging. We present some illustrative examples.