A Bayesian Network Based Framework for Multi-criteria Decision Making

Multi-Criteria Decision Making (MCDM) involves the selection of the best actions from a set of alternatives, each of which is evaluated against multiple, and often conflicting, criteria. Most of the existing MCDM methods only focus on decisions under certainty. The criteria were evaluated separately as if they were independent of each other. Complex, often uncertain interactions between criteria, and between criteria and other factors are not modeled in a coherent and systematic manner. To address these issues, we propose in this paper a decision framework based on Bayesian networks (BN) and influence diagram (ID) to structure and manage MCDM problems with explicit modeling of uncertain interactions among entities of interest. In this framework, a decision problem is represented by an ID where each decision node represents the set of alternatives for a decision, a utility node represents the set of objectives (decision maker’s preferences), decision criteria and internal or external factors that may affect the criteria are represented by chance nodes. Interdependencies among these nodes are qualitatively modeled by the links in the diagram and quantitatively by conditional probability tables (CPT) associated with each of the chance nodes and the utility node. The joint probability distribution, which is compactly captured by the network structure and CPT, encodes the domain expert’s knowledge of interdependency between variables. The decision problem is then treated as an optimization problem: recommend the decision alternative which optimizes the expected utility, given observations of some external factors and preferences made by the decision maker. Various algorithms developed for BN and ID can be employed to automatically solve this problem. The steps that need to be taken to model a MCDM problem as an ID is presented, illustrated with a running example. Other related issues are also discussed. Our preliminary work indicates that this framework is of great potential as a modeling tool to support MCDM decision making in an uncertain environment.