An Interpretable Fuzzy Classifier Learned Through Soft-Margin Minimization with Transparent Fuzzy Sets

This paper proposes an interpretable fuzzy classifier learned through soft-margin minimization (IFC-SMM) with the consideration of fuzzy set transparency. The rules of the IFC-SMM are built through a firing-strength-based clustering method. Parameters in the IFC-SMM are learned through SMM to endow the fuzzy classifier (FC) with high generalization ability. Based on the SMM, the antecedent and consequent parameters in the built rules are learned through the gradient descent algorithm and support vector machine (SVM), respectively. To improve the interpretability of the IFC-SMM, two constraints imposed on fuzzy set transparency are introduced into the SMM in the tuning of the antecedent parameters. Experimental results on real classification problems with comparisons with different FCs show the characteristics of the IFC-SMM.

I. Introduction

Fuzzy classifiers (FCs) that comprise fuzzy if-then rules have been extensively applied to different classification problems, ranging from image classification [1], [2] to medical diagnosis [3]–[5]. To automate the design of FCs, many data-driven learning approaches have been proposed. Among the various alternative learning approaches, a popular one is neural FCs that optimize fuzzy rules through neural learning [4], [6]–[9]. Another popular approach is evolutionary FCs that optimize fuzzy rules through evolutionary computation techniques, such as genetic algorithms [1], [10]–[13]. These approaches optimize fuzzy rules by minimizing an objective function typically defined as the classification error of training patterns. Minimization of training error does not imply good test performance and may face the overtraining problem. Therefore, the test performance of neural and evolutionary FCs may be unsatisfactory.