A new Takagi–Sugeno–Kang model to time series forecasting

A fuzzy inference system consists of a machine learning concept that combines accuracy and interpretability. They are divided into two main groups: Mamdani and Takagi–Sugeno-Kang. While Mamdani models favor interpretability, Takagi–Sugeno-Kang models provide more accurate results because of their ability to approximate a nonlinear system through a collection of linear subsystems. The evolving Takagi Sugeno model inspired a new class of Takagi–Sugeno-Kang models classified as an evolving fuzzy system, which can update their structure and functionality to adapt themselves to changes in the data. However, these models may provide several rules that reduce the interpretability. Furthermore, as they usually present many hyper-parameters, it can be challenging to obtain results that satisfy specific requirements in terms of the accuracy-interpretability trade-off. To overcome such shortcomings, this paper introduces a new model in which the only hyper-parameter is the maximum number of rules. Consequently, the user can define the number of rules considering the accuracy-interpretability trade-off. The introduced models are evaluated using benchmark time series, three well-known financial series, S&P 500, NASDAQ, and TAIEX, and renewable energy datasets. The results are compared with other state-of-the-art machine learning models, such as classical models and some rule-based evolving Fuzzy Systems. The results are evaluated regarding error metrics and the number of final rules. The proposed model obtained similar or equal performance in the simulations to the compared models with increased interpretability. The code of the proposed model is available at https://github.com/kaikerochaalves/NTSK.git.