Extraction of fuzzy rules from support vector machines

The relationship between support vector machines (SVMs) and Takagi–Sugeno–Kang (TSK) fuzzy systems is shown. An exact representation of SVMs as TSK fuzzy systems is given for every used kernel function. Restricted methods to extract rules from SVMs have been previously published. Their limitations are surpassed with the presented extraction method. The behavior of SVMs is explained by means of fuzzy logic and the interpretability of the system is improved by introducing the λ-fuzzy rule-based system (λ-FRBS). The λ-FRBS exactly approximates the SVM's decision boundary and its rules and membership functions are very simple, aggregating the antecedents with uninorms as compensation operators. The rules of the λ-FRBS are limited to two and the number of fuzzy propositions in each rule only depends on the cardinality of the set of support vectors. For that reason, the λ-FRBS overcomes the course of dimensionality and problems with high-dimensional data sets are easily solved with the λ-FRBS.