Evolving Complex-Valued Interval Type-2 Fuzzy Inference System

Abstract

Interval Type-2 fuzzy systems have been shown to be extremely capable of handling vagueness as well as uncertainty in data, while complex-valued fuzzy sets have been demonstrated to be capable of solving classification problems efficiently. This paper combines their collective advantage to propose a complex-valued Interval Type-2 Fuzzy Inference System (referred to as CIT2FIS). To derive the fuzzy rules, a Recursive Least Squares based algorithm is proposed. The proposed algorithm evolves (add/ prune) and adapts the rules in an evolving online fashion. During sequential learning, the network monitors the error and knowledge contained in the current sample and either rules are evolved (added, pruned) to capture the knowledge in the sample, or the rule parameter updated. Upon rule addition, the centers are determined based on the current input and the output weights are analytically determined such that a least squares fit is obtained. This ensures that the rule retain its interpretability and accuracy. Parameter update is based on recursive least squares based approach. In order to maintain the parsimony of the network, a data-driven rule pruning scheme is employed. To further enhance the generalization ability of the network, wellknown meta-cognitive learning mechanism is employed in this work. The performance of the proposed CIT2FIS is evaluated on a set of real-valued classification problems. The performance comparison with other state-of-the-art complex-valued as well as fuzzy classifiers clearly highlights the advantage of the proposed work.