IFC-Filter: Membership function generation for inductive fuzzy classification

Fuzzy classification can be defined as a method of computing the degrees of membership of objects in classes. There are many approaches to fuzzy classification, most of which generate sophisticated multivariate models that classify all of the input space simultaneously. In contrast, methods for membership function generation (MFG) derive simple models for fuzzy classification that map one input variable to one fuzzy class; therefore, by minimizing complexity, these models are very understandable to human experts. The unique contribution of this paper is a method for membership function generation from real data that is based on inductive logic. Most existing MFG methods apply either parameter optimization heuristics or unsupervised learning and clustering for the definition of the membership function. In contrast to heuristic methods, our method can approximate membership functions of any shape. In comparison to clustering, our approach can make use of a target signal to learn a membership function supervised from the association between two variables. Compared to probabilistic methods, which translate frequency information, i.e., normalized histograms, directly into membership degrees, our approach applies inductive reasoning based on conditional relative frequencies, which are called likelihoods. According to the law of likelihood in inductive logic, it is the ratio between the likelihoods of the data that is of interest when evaluating two alternative hypotheses, not the likelihoods themselves. The greatest advantage of our method is its understandability to human users and thereby the potential for visual analytics. However, experimental evaluation did not show reproducible significant effects on the predictive performance of conventional multivariate regression models. Given that there are already many very accurate multivariate models for fuzzy classification, the practical implication is that IFC-Filter can unfold its unique potential mainly for explaining data, specifically, associations between analytical and target variables, to human decision makers. Lessons learned from two case studies with industry partners demonstrate that IFC-Filter can extract interpretable and actionable knowledge from data.