On support vector regression machines with linguistic interpretation of the kernel matrix

Initially, the idea of approximate reasoning using generalized modus ponens and a fuzzy implication is recalled. Next, a fuzzy system based on logical interpretation of if–then rules and with parametric conclusions is presented. Then, it is shown that global and local ε-insensitive learning of the above fuzzy system may be presented as the learning of a support vector regression machine with a special type of a kernel matrix obtained from clustering. The kernel matrix may be interpreted in terms of linguistic values based on the premises of if–then rules. A new method of obtaining a fuzzy system by means of a support vector machine (SVM) with a data-dependent kernel matrix is introduced. This paper contains examples of a SVM used to design fuzzy models of real-life data. Simulation results show an improvement in the generalization ability of a fuzzy system learned by the new method compared with traditional learning methods.