Decision-Making with Risk under Interval Uncertainty Based on Area Metrics

From the perspective of D-S evidence theory and area measurement, a risk-based comprehensive decision-making method that considers both the expected utility and the uncertainty of the scheme is proposed under the interval uncertainty environment of attribute values. The upper and lower bounds of the synthetic probability distribution of attributes values in different natural states are constructed based on the belief measure and plausibility measure. Based on the area measurement, a method for calculating the expected utility of each scheme is proposed. To reflect the influence of the uncertainty in the evaluation value of each scheme attribute on the final decision result, two indexes are defined: the evaluation uncertainty of attributes (EUA) and the uncertainty of the expected utility of scheme (UEU). Finally, considering the expected value of the expected utility and its uncertainty, three decision methods, namely, risk-neutral, risk-averse, and risk-preference, are constructed. An example is considered to show that the proposed method is effective and practical, and the uncertainty of the expected utility has a significant impact on the result of risky decisions. The new method can solve the problems of existing methods that overlook the impact of epistemic uncertainty on the decision-making process.