Study on equality conditions of fuzzy rule-based classification systems to radial basis functions,SVM and nearest neighbor classifiers

There are some well-known classifiers which in special conditions, not only have a similar structure, but also show equal behavior in classifying any instance. This paper is aimed at theoretically investigate and review the conditions in which, Fuzzy Rule-Based Classification Systems (FRBCS) are equal to three commonly used classifiers: Radial Basis Function (RBF) networks, K-Nearest Neighbors (K-NN) and Support Vector Machines (SVM). Based on this study, the learning algorithms, objective functions and any innovation in those classifiers can be used in FRBCS and vice versa. The equality conditions are defined based on properties such as membership function, T-norm, reasoning method, type of the fuzzy rules, distance or similarity functions and kernels.