caa a22 4500 463187199 CHVBK 20180406164857.0 cr unu---uuuuu 170326e20070401xx s 000 0 eng 10.1007/s10472-007-9052-7 doi (NATIONALLICENCE)springer-10.1007/s10472-007-9052-7 Derivative of functions over lattices as a basis for the notion of interaction between attributes [Elektronische Daten] [Michel Grabisch, Christophe Labreuche] 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. Springer Science+Business Media B.V., 2007 Interaction index nationallicence Shapley value nationallicence Capacity nationallicence Game nationallicence Lattice nationallicence Discrete derivative nationallicence Grabisch Michel Université Paris I - Panthéon-Sorbonne, Paris, France aut Labreuche Christophe Thales Research & Technology, Domaine de Corbeville, 91404, Orsay Cedex, France aut Annals of Mathematics and Artificial Intelligence Springer Netherlands 49/1-4(2007-04-01), 151-170 1012-2443 49:1-4<151 2007 49 10472 https://doi.org/10.1007/s10472-007-9052-7 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s10472-007-9052-7 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Grabisch Michel Université Paris I - Panthéon-Sorbonne, Paris, France aut NATIONALLICENCE 700 1- Labreuche Christophe Thales Research & Technology, Domaine de Corbeville, 91404, Orsay Cedex, France aut NATIONALLICENCE 773 0- Annals of Mathematics and Artificial Intelligence Springer Netherlands 49/1-4(2007-04-01), 151-170 1012-2443 49:1-4<151 2007 49 10472 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer