Fuzzy (c+p)-Means Clustering and Its Application to a Fuzzy Rule-Based Classifier: Toward Good Generalization and Good Interpretability

This paper introduces a new classifier design method based on a modification of the classical fuzzy c-means clustering. First, a new fuzzy $c$-means clustering with p constant prototypes is proposed. This method can be considered a generalization of the concept of the conditional fuzzy clustering with some prototypes a priori known. A special initialization of the prototypes is introduced. Next, the proposed clustering method is used to construct the premises of an if-then rule-based classifier. The conclusions of these rules are obtained by minimization of a criterion function with various approximations of a misclassification error (e.g., based on the quadratic, the linear, the sigmoidal or the Huber's loss function). The conjugate gradient algorithm is used to minimize the proposed criterion function. Each if-then rule is represented in the Mamdani-Assilan form, which has good interpretability. Finally, an extensive experimental analysis on 14 benchmark datasets is performed to demonstrate the validity of the classifier introduced. Its competitiveness to the state-of-the-art classifiers, with respect to both performance and interpretability, is also shown.