In this paper, we propose an evolving Interval Type-2 Neuro-Fuzzy Inference System (IT2FIS) and its fully sequential learning algorithm. IT2FIS employs Interval Type-2 fuzzy sets in the antecedent part of each rule and the consequent realizes Takagi-Sugeno-Kang (TSK) fuzzy inference mechanism. In order to render the inference fast and accurate, we propose a data-driven interval-reduction approach to convert Interval Type-1 fuzzy set in antecedent to Type-1 fuzzy number in the consequent. During learning, the sequential algorithm learns a sample one-by-one and only once. IT2FIS structure evolves automatically and adapts its network parameters using metacognitive learning mechanism concurrently. The meta-cognitive learning regulates the learning process by appropriate selection of learning strategies and helps proposed IT2FIS to approximate the input-output relationship efficiently. An evolving IT2FIS employing a meta-cognitive learning algorithm is referred to as McTI2FIS. Performance of McIT2FIS is evaluated using a set of benchmark time-series problems and is compared with existing Type-2 and Type-1 fuzzy inference systems. Finally, the performance of proposed McIT2FIS has been evaluated using a practical stock price tracking problem. The results clearly highlight that McIT2FIS performs better than other existing results in the literature.
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