Hierarchical aggregation functions generated from belief structures

We deal with the development of tools useful for the construction of multicriteria decision functions that allow for the modeling of the types of complexity that is the hallmark of human intelligence. We first discuss the fuzzy measure, describe its potential for characterizing relationships between multiple criteria, and introduce the class of ordered aggregation functions that can be based on a fuzzy measure. We then focus on the two fuzzy measures associated with the Dempster-Shafer belief structure, plausibility, and belief, and describe the types of ordered aggregation functions obtained using these measures. This leads us to introduce a new class of aggregation functions obtained by allowing a decision maker to provide his decision imperative in terms of components (concepts) that contribute to his overall satisfaction. Each component consists of a value, a subset of criteria and an agenda for combining the criteria in the component. Finally, it is shown how these components can be combined to allow for the representation of hierarchical decision functions