Abstract
This paper extends the previous work in the connection between fuzzy classifiers and kernel machines [2] to a general case. In [2], all membership functions for the same input variable are generated from location transformation of a reference function. A translation invariant kernel is constructed from reference functions. The kernel is a Mercer kernel if the reference functions are positive definite. A support vector learning approach for positive definite fuzzy classifiers (PDFCs) was proposed.
In this paper, a smooth support vector learning algorithm for fuzzy rule-based classification systems is proposed. The smooth support vector machine (SSVM) is capable of generating nonlinear separating surfaces using arbitrary kernels. The positive definiteness requirement on reference functions is relaxed. A fuzzy classifier using arbitrary reference functions can be built from the training samples based on an SSVM. The resulting fuzzy classifier is called standard binary fuzzy classifier (SBFC). Fuzzy rules are extracted with each rule given by a training sample. The reduced kernel technique is introduced to simplify the decision function of the SBFC and to reduce the number of fuzzy rules. Finally, the performance of SBFCs with different reference functions is illustrated by experimental results. Comparisons with PDFCs are also provided.