Potential optimality and robust optimality in multiattribute decision analysis with incomplete information: A comparative study

The traditional approach for multiple attribute decision analysis with incomplete information on alternative values and attribute weights is to identify alternatives that are potentially optimal. However, the results of potential optimality analysis may be misleading as an alternative is evaluated under the best-case scenario of attribute weights only. Robust optimality analysis is a conservative approach that is concerned with an assured level of payoff for an alternative across all possible scenarios of weights. In this study, we introduce two measures of robust optimality that extend the robust optimality analysis approach and classify alternatives in consideration into three groups: strong robust optimal, weak robust optimal and robust non-optimal. Mathematical models are developed to compute these measures. It is claimed that robust optimality analysis and potential optimality analysis together provide a comprehensive picture of an alternative's variable payoff.

► RO — robust optimality; PO — potential optimality.
► PO analysis results may be misleading as it considers the best-case scenario of weights.
► RO analysis is extended to deal with imprecise information of values and weights.
► The measure of weak robust optimality is defined and interpreted.
► Integrating the results of PO analysis and RO analysis is critical.