Monotone decomposition of 2-additive Generalized Additive Independence models

Journal article: The GAI (Generalized Additive Independence) model proposed by Fishburn is a generalization of the additive value function model, which need not satisfy preferential independence. Its great generality makes however its application and study difficult. We consider a significant subclass of GAI models, namely the discrete 2-additive GAI models, and provide for this class a decomposition into nonneg-ative monotone terms. This decomposition allows a reduction from exponential to quadratic complexity in any optimization problem involving discrete 2-additive models, making them usable in practice.

Author(s)

Michel Grabisch, Christophe Labreuche

Journal
  • Mathematical Social Sciences
Date of publication
  • 2018
Keywords
  • Generalized additive independence
  • Capacity
  • Multicriteria decision making
  • Multichoice game
  • Conjoint measurement
Pages
  • 64-73
Version
  • 1
Volume
  • 92