Independence concepts in evidence theory

Authors:
Inés Couso;Serafín Moral
Affiliations:
Dep. of Statistics and O.R., University of Oviedo, Spain;Dep. of Computer Sciences and A.I., University of Granada, Spain
Venue:
International Journal of Approximate Reasoning
Year:
2010

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Abstract

We study three conditions of independence within evidence theory framework. The first condition refers to the selection of pairs of focal sets. The remaining two ones are related to the choice of a pair of elements, once a pair of focal sets has been selected. These three concepts allow us to formalize the ideas of lack of interaction among variables and among their (imprecise) observations. We illustrate the difference between both types of independence with simple examples about drawing balls from urns. We show that there are no implication relationships between both of them. We also study the relationships between the concepts of ''independence in the selection'' and ''random set independence'', showing that they cannot be simultaneously satisfied, except in some very particular cases.