A new approach in model selection using fuzzy decision making-a trade off between probability and possibility theories

Model selection problem is applied to many various fields of scientific studies, in order to corroborate or verify a theory, or in order to prefer one theory among a set of competing hypothesis. Different criteria are taken as basis to select one model between several parallel models in both statistical and visual types. This paper proposes a new method in model selection based on solution of a Fuzzy Decision-Making (FDM) problem. The method enables the scientist (model builder) to apply all desired validity criteria, even linguistic criteria, systematically by defining a proper Possibility Distribution Function (PDF) due to each criterion. Finally, minimization of a utility function composed of the PDFs will determine the best selection.