Identification of non-additive measures form sample data

Pedro Miranda , Michel Grabisch (1) , Pedro Gil

1 SYSDEF - Systèmes d'aide à la décision et à la formation

Non-additive measures have become a powerful tool in Decision Making. Therefore, a lot of problems can be solved through the use of Choquet integral with respect to a non-additive measure. Once the decision maker decides to use this criterion in his decision process, next step is to build the non-additive measure up. In this paper we solve the problem of learning the measure from sample data by minimizing the squared error. We study the conditions for the unicity of solution, as well as the set of solutions. A particular family of non-additive measures, the so-called k-additive measures, are specially appealing due to their simplicity and richness. We will use 2-additive measures in a practical case to show that k-additive measures can be considered as a good approximation of general measures.

Domaines: Informatique [cs]

Pedro Miranda, Michel Grabisch, Pedro Gil. Identification of non-additive measures form sample data. Planning based on decision theory, 472, Springer, pp.43-63, 2003, International Centre for Mechanical Sciences, ⟨10.1007/978-3-7091-2530-4_3⟩. ⟨hal-01533739⟩