Selection of a representative decision recommendation using a set of value functions

Purpose In multi-criteria ranking problems, the UTA-like methods can be used to infer the value functions that restore the decision-maker’s (DM’s) indirect preference information. These value functions represent all possible preference systems for the DM. In this paper, we aim to develop a method for determining the complete ranking of alternatives based on all such value functions. Design/methodology/approach We extend the DM’s inductive preference for value functions in the selection of a representative value function to rankings of alternatives and construct a novel measure referred as the representativeness index to evaluate the performance of rankings relative to the inductive preference. Subsequently, by exploring all value functions that are capable of generating a ranking, two robust representativeness indices are constructed and a simulation algorithm is proposed for calculating the robust representativeness index. Findings Determining the ranking based on the representative value function can be seen as selecting the ranking with the largest representativeness index. Additionally, we find through a case study that the ranking determined based on robust representativeness indices has good robustness in the sense of inductive preferences. Originality/value The inductive preference is a manifestation of the DM’s preference system. This paper proposes a method for measuring the performance of rankings relative to inductive preferences. The performance of a ranking is defined as the performance of all value functions that can produce that ranking relative to the inductive preference. In turn, it is possible to identify the ranking that best matches the DM’s preference system.