Derivative of functions over lattices as a basis for the notion of interaction between attributes

Details Derivative of functions over lattices as a basis for the notion of interaction between attributes Derivative of functions over lattices as a basis for the notion of interaction between attributes

2007-11-14

arxiv.org/abs/0711.2115v1

Annals of Mathematics and Artificial Intelligence 49 (2007) 151-170

Computer Science

Discrete Mathematics

Scientific paper

The paper proposes a general notion of interaction between attributes, which can be applied to many fields in decision making and data analysis. It generalizes the notion of interaction defined for criteria modelled by capacities, by considering functions defined on lattices. For a given problem, the lattice contains for each attribute the partially ordered set of remarkable points or levels. The interaction is based on the notion of derivative of a function defined on a lattice, and appears as a generalization of the Shapley value or other probabilistic values.

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