Fuzzy Operator Trees for Modeling Rating Functions

We introduce a new method for modeling rating (utility) functions which employs techniques from fuzzy set theory. The main idea is to build a hierarchical model, called a fuzzy operator tree (FOT), by recursively decomposing a rating criterion into sub-criteria, and to combine the evaluations of these sub-criteria by means of suitable aggregation operators. Apart from the model conception itself, we propose an evolutionary method for model calibration that fits the parameters of an FOT to exemplary ratings. The possibility to adapt an FOT to a given set of data makes the approach also interesting from a machine learning point of view.