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In group decision making, different experts often think about the same problem in quite different ways. They frequently have different opinions for decision making about the same situation. Using a Bayesian network structure for optimizing problems, different experts who work as a group for projects may have different solutions for indentifying the causal relationships among variables in the BN model and quantifying graphical models with numerical probabilities. For example, expert-1 may state that “making a decision in situation A causes situation B and making a decision in situation B causes situation C”. But expert-2 may state that “making a decision in situation B causes situation A and making a decision in situation A causes situation C”. Even in a simple case of decision making, the expert knowledge obtained from different experts is quite different. It is typically not possible to avoid contradictions among different expert’s solutions in group decision making. In this article, we propose a practical framework and a methodology for transforming expert knowledge or final group decision making statements into a set of qualitative statements and probability inequality constraints for inference in a Bayesian Network. First, we need to identify a set of alternatives on which the experts have opinions and then consider the problem of constructing a group preference ranking. If such a group preference ranking can be created, then one could utilize the alternative at the top of the ranked list the alternative preferred by the group. Second, after we obtain the most preferred alternative or statement such as “A causes B and then B causes C” from the group decision making, we propose a formal method to transform knowledge, represented by a set of qualitative statements, into an a priori distribution for Bayesian probabilistic models. The mathematical equation for Bayesian inference is derived based on knowledge obtained from the final group decision statements. The set of model parameters, consistent with the statements, and the distribution of models in the structure-dependent parameter space are presented. We also propose a simplified method for constructing the “a priori” model distribution. Each statement obtained from the experts is used to constrain the model space to the subspace which is consistent with the statement provided. Finally, we present qualitative knowledge models and then show a complete formalism of how to translate a set of qualitative statements into probability inequality constraints. Several cases of Bayesian influence are classified and the probability inequality constraints presented in each case are described. 5 |
