A Robust Additive Multiattribute Preference Model using a Nonparametric Shape-Preserving Perturbation

This paper develops a multiattribute preference ranking rule in the context of utility robustness. A nonparametric perturbation of a given additive reference utility function is specified to solve the problem of ambiguity and inconsistency in utility assessments, while preserving the additive structure and the decision maker’s risk preference under each criterion. A concept of robust preference value is defined using the worst expected utility of an alternative incurred by the perturbation, and we rank alternatives by comparing their robust preference values. An approximation approach is developed using Bernstein polynomials to solve the robust preference value. The constructed approximation problem is reformulated as a quadratic constrained linear program (QCP), and the bound of the approximation error is analyzed. An integrated energy distribution system planning problem is used to illustrate the usefulness of the robust ranking rule and the instability of the decision based on the expected utility theory.