Constructing kernels by fuzzy rules for support vector regressions

This study focuses on designing a new class of kernels to incorporate the prior information into the training process of support vector regressions. The prior information in the form of fuzzy rules is considered for regression problems. First, the antecedent of each fuzzy rule is represented by some fuzzy equivalence relations. Moreover, the properties of kernels and pseudo-metrics are employed to discuss the conditions for fuzzy equivalence relations to be kernels. Then the kernels for each of the fuzzy rules are obtained by using the given additive generators and arbitrary pseudo-metrics as well as triangular norms. Furthermore, a class of kernels is obtained by linearly combining the kernels corresponding to each rule via fuzzy entropies for all the fuzzy rules. Finally, we apply this class of kernels to support vector regressions. The experimental results help quantify the performance of the proposed approach.