Extending the macsum aggregation to interval-valued inputs

Due to a lack of information or access to the data, or simply due to the imprecise nature of the data, there are cases where a function that maps intervalvalued inputs is more appropriated to model a system. With the concern to keep the advantageous properties of the Choquet integral, we propose here a model that maps interval-valued inputs onto intervalvalued outputs whose upper and lower bounds are Choquet integrals with respect to a parametric set function. This model is an extension to intervalvalued inputs of the macsum aggregation proposed in [15]. In this article, we show that this extension can be easily computed thanks to some properties of the macsum parametric set function.