A Metacognitive Complex-Valued Interval Type-2 Fuzzy Inference System

Abstract

This paper presents a complex-valued interval type-2 neuro-fuzzy inference system (CIT2FIS) and derive its metacognitive projection-based learning (PBL) algorithm. Metacognitive CIT2FIS (Mc-CIT2FIS) consists of a CIT2FIS, which realizes Takagi-Sugeno-Kang type inference mechanism, as its cognitive component. A PBL with self-regulation is its metacognitive component. The rules of CIT2FIS employ interval type-\(2~q\) -Gaussian membership functions that can represent different radial basis functions for different values of \(q\) . As each sample is presented to the network, the metacognitive component monitors the hinge-loss error and class-specific knowledge potential of the current sample to efficiently decide on what-to-learn, when-to-learn, and how-to-learn it. When a new rule is added or existing rules are updated, the optimal parameters of CIT2FIS corresponding to the minimum of the hinge-loss error function are computed using a PBL algorithm derived using the Wirtinger calculus. The performance of Mc-CIT2FIS is evaluated on a set of benchmark real-valued classification problems from the UCI machine learning repository. A circular transformation is used to convert the real-valued features to the complex-valued features in these problems. The performance comparison and statistical study clearly show the superior classification ability of Mc-CIT2FIS. Finally, the proposed complex-valued network is used to solve a practical human action recognition problem that is represented by complex-valued optical flow-based feature set, and a human emotion recognition problem represented using complex-valued Gabor filter-based features. The performance results on these problems substantiate the superior classification ability of Mc-CIT2FIS.