A Bayesian evaluation of fuzzy logic in a classification problem

Models based on fuzzy sets are increasingly being used in academic and industrial research and applications, primarily for data analysis and systems control. The possible consequences of their popular use necessitate their evaluation from a probabilistic viewpoint. In this paper, a simple fuzzy logic model is translated into a Bayesian setting and used to address a discrimination and attribution (or classification) problem. Probabilistic tools and concepts are then employed to evaluate the fuzzy-set paradigm. The translation suggests that applications of fuzzy-set theory may suffer from many serious problems, primarily due to the unobservability of the fuzzy-set membership vector and to the poor structure of the fuzzy-set model. These difficulties are illustrated using the well-known Fisher iris data. For example, Table 11 suggests that fuzzy-set models may find probabilistic mixtures only when the evidence is thoroughly overwhelming in Bayesian models.