Bonferroni Mean With Weighted Interaction

Bonferroni mean aggregates the interaction between all pairs of inputs from some n-dimensional input vector. Therefore, it is able to capture the dependency structure between the inputs. Weighted version of the Bonferroni mean then assumes that each input has a possibly different weight. Such an approach poses several constraints that decrease the modeling flexibility of the dependency structure on the input space. In this paper, we present an overview of the different approaches to weighted Bonferroni mean and introduce the Bonferroni mean with weighted interaction where interactions between inputs are weighted rather than the inputs themselves. We show several important properties of the Bonferroni mean with weighted interaction and its connection to concepts studied before. Finally, using the described approach we design a system for emergency management that is able to raise an alarm in the case where certain criteria are met.