eT2FIS: An Evolving Type-2 Neural Fuzzy Inference System

There are two main approaches to design a neural fuzzy system; namely, through expert knowledge, and through numerical data. While the computational structure of a system is manually crafted by human experts in the former case, self-organizing neural fuzzy systems that are able to automatically extract generalized knowledge from batches of numerical training data are proposed for the latter. Nevertheless, both of these approaches are static where only parameters of a system are updated during training. On the other hand, the demands and complexities of real-life applications often require a neural fuzzy system to adapt both its parameters and structure to model the changing dynamics of the environment. To counter these modeling bottlenecks, intense research efforts are subsequently channeled into the studies of evolving/online neural fuzzy systems. There are generally two classes of evolving neural fuzzy systems: the Takagi–Sugeno–Kang (TSK) systems and the Mamdani systems. While most existing literature consists of evolving Type-1 TSK-typed and Type-1 Mamdani-typed models, they may not perform well in noisy environment. To improve the robustness of these neural fuzzy systems, recent efforts have been directed to extend evolving Type-1 TSK-typed neural fuzzy systems to Type-2 models because of their better known noise resistance abilities. In contrast, minimum similar effort has been made for evolving Mamdani-typed models. In this paper, we present a novel evolving Type-2 Mamdani-typed neural fuzzy system to bridge this gap. The proposed system is named evolving Type-2 neural fuzzy inference system (eT2FIS), and it employs a data-driven incremental learning scheme. Issues involving the online sequential learning of the eT2FIS model are carefully examined. A new rule is created when a newly arrived data is novel to the present knowledge encrypted; and an obsolete rule is deleted when it is no longer relevant to the current environment. Highly over-lapping fuzzy labels in the input–output spaces are merged to reduce the computational complexity and improve the overall interpretability of the system. By combining these three operations, eT2FIS is ensured a compact and up-to-date fuzzy rule base that is able to model the current underlying dynamics of the environment. Subsequently, the proposed eT2FIS model is employed in a series of benchmark and real-world applications to demonstrate its efficiency as an evolving neural fuzzy system, and encouraging performances have been achieved.