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Decision‐making under uncertainty through extending influence diagrams with interval‐valued parameters

Influence diagrams (IDs) are one of the most commonly used graphical and mathematical decision models for reasoning under uncertainty. In conventional IDs, both probabilities representing beliefs and utilities representing preferences of decision makers are precise point‐valued parameters. However, it is usually difficult or even impossible to directly provide such parameters. In this paper, we extend conventional IDs to allow IDs with interval‐valued parameters (IIDs) and develop a counterpart method of Copper's evaluation method to evaluate IIDs. IIDs avoid the difficulties attached to the specification of precise parameters and provide the capability to model decision‐making processes in a situation that the precise parameters cannot be specified. The counterpart method to Copper's evaluation method reduces the evaluation of IIDs into inference problems of Bayesian networks with interval‐valued probabilities. An algorithm based on the approximate inference of Bayesian networks with interval‐valued probabilities is proposed, and extensive experiments are conducted. The experimental results indicate that the proposed algorithm can find the optimal strategies effectively in IIDs, and the interval‐valued expected utilities obtained by proposed algorithm are contained in those obtained by exact evaluating algorithms. The newly development approach would significantly extend the range of IDs for managerial decision support applications where parameters of variables can be specifically defined by only estimated intervals.