Maddalena Manzi

Ultramodular aggregation functions

Ultramodular aggregation functions are investigated and discussed, including a study of structural properties and the proposal of some construction methods.

Ultramodularity and copulas

Ultramodular binary copulas are discussed, i.e., copulas of a random vector whose components are mutually stochastically decreasing with respect to each other. The additive generators of Archimedean ultramodular binary copulas are fully characterized. Finally, a new construction method for binary copulas based on n-ary ultramodular aggregation functions is proposed.

Aggregation functions with stronger types of monotonicity

Following the ideas of stronger forms of monotonicity for unary real functions and for capacities,k-monotone and stronglyk-monotone aggregation functions are introduced and discussed. In the special casek= 2 also some applications are given.

Supermodular Binary Aggregation Operators and Copulae

This paper presents the role of copula functions in the theory of aggregation operators. In this context we are focusing our attention about several properties of aggregation functions, like supermodularity and Schur-concavity, studying also a decomposition of supermodular binary aggregation operators and copulae.