A Systematic Fuzzy Decision-Making Process to Choose the Best Model Among a Set of Competing Models

The assessment of a theory is the main objective of scientists. Theories are always introduced by models, and model selection is applied to many various fields of scientific studies in order to corroborate or verify the theory as the winning one among a set of competing hypotheses. Different criteria are taken as bases to select one model among several parallel models in both statistical and visual types. This paper proposes a new method in model selection based on the solutions of a fuzzy decision-making problem. The method enables us to apply systematically all desired validation criteria by defining a proper possibility distribution function (PDF) for each criterion. The generality of the method allows us to consider even intuitive, inaccurate, or linguistic criteria. Finally, the maximization of a utility function, rationally composed of the PDFs, will determine the best choice of competing models. The method is illustrated by two sets of linear and nonlinear parallel models.