Dealing with external actions in belief causal networks

Graphical models are efficient and simple ways to represent dependencies between variables. We introduce in this paper the so-called belief causal networks where dependencies are uncertain causal links and where the uncertainty is represented by belief masses. Through these networks, we propose to represent the results of passively observing the spontaneous behavior of the system and also evaluate the effects of external actions. Interventions are very useful for representing causal relations, we propose to compute their effects using a generalization of the “do” operator. Even if the belief chain rule is different from the Bayesian chain rule, we show that the joint distributions of the altered structures to graphically describe interventions are equivalent. This paper also addresses new issues that are arisen when handling interventions: we argue that in real world applications, external manipulations may be imprecise and show that they have a natural encoding under the belief function framework.

► Modeling causality is important in the belief function framework.
► Belief causal networks: the treatment of interventions is different from observations.
► Interventions as making changes in the structure of the network.
► Equivalence between belief graph augmentation and belief graph mutilation.
► Within belief functions theory, imprecise interventions are naturally en coded.
► Multigranulation decision-theoretic rough sets are proposed.
► When parameters satisfy some constraints, it will derive many kinds of multigranulation rough sets.
► The relationships among multigranulation decision-theoretic rough sets, decision-theoretic rough sets and single granulation rough sets are established.