Fuzzy UTASTAR: A method for discovering utility functions from fuzzy data

We propose Fuzzy UTASTAR, a method for inferring fuzzy utility functions from a partial preorder of options evaluated on multiple criteria. It is an extension of the well-known UTASTAR method capable to handle both ordinary (crisp) and fuzzy evaluation data. This property gives much flexibility to decision makers because the majority of real-life decision problems involve a considerable level of uncertainty that hinders them from assigning exact evaluations (scores) to options. In case all evaluation data are crisp the method behaves exactly as the original UTASTAR. The proposed method builds fuzzy additive value functions taking as input a partial preorder on a subset of the options, called reference set, along with their associated scores on the criteria. The resulting fuzzy utility functions can subsequently be used to estimate the (fuzzy) utility of each option, thus allowing their ranking, prioritization, selection or classification. The ranking of the options in partial preorder is as compatible as possible to the original one. The method is implemented into a decision support system and is applied to an example from the transportation domain. Results are found to be in concordance with those of the original method. To the best of our knowledge this is the first attempt to extend UTASTAR method to handle both crisp and fuzzy evaluation data.