An Evidential Measure of Risk in Evidential Markov Chains

This paper provides a new method for computing a risk criterion for decision-making in systems modelled by an Evidential Markov Chain (EMC), which is a generalization to the Dempster-Shafer's Theory of Evidence [1]: it is a Markov chain manipulating sets of states instead of the states themselves. A cost is associated to each state. An evidential risk measurement derived from the statistical ones will be proposed. The vector of the costs of the states, the transition matrix of the Markov model, and the gauge matrix describing the repartition of the sets will be used to construct matrix calculations in order to provide an upper and a lower bound of the estimated risk. The former is a Choquet integral following the belief function, and the latter is established from the plausibility function.

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