## 1 Introduction  
Fuzzy systems (FSs) originated from the fuzzy set theory proposed by [PERSON] in 1965 [1], which are based on fuzzy rules. FSs are more interpretable and intuitive methods that can match any set of input-output data by each fuzzy rule [2]. As soft computing techniques, FSs have achieved great success in dealing with numerous problems of uncertainty, such as the seismic vulnerability assessment of buildings [3, 4, 5], the prediction of the irrigation water infiltration rate [6], the automatic classification of crop disease images [7], etc. However, there are three main challenges in developing optimal FSs through the analysis of the research status: (1) Optimization: Optimizing FSs within a valid period of time to achieve higher accuracy and faster convergence is now worthy of in-depth study, which is also challenging. (2) The curse of dimensionality: The number of fuzzy rules increases exponentially with the dimensionality of the input, which leads to the computation not being able to be completed within a reasonable time. Hence, it is difficult for FSs to deal with high-dimensional problems. (3) Interpretability: The interpretability is the advantage of FSs that distinguishes them from other machine learning models. However, as the number of fuzzy rules increases, the interpretability of FSs will be affected. Therefore, how to solve the high-dimensional problem on the basis of ensuring better interpretability is one of the current bottlenecks. In recent years, great efforts have been made to improve FSs [8]. Evolutionary algorithms (EAs) [9; 10], the gradient descent (GD) algorithm [11], and GD plus least squares estimation (LSE) [12] have been proposed to optimize FSs. Although EAs can search for the optimal solution with enough iterations, the computational cost is too expensive to be suitable for the optimization of FSs. The adaptive neuro-fuzzy inference system (ANFIS) proposed by [PERSON] formed by GD plus LSE [12] has been widely applied in national energy demand forecasting [13; 14], flood sensitivity forecasting [15], geographic temperature forecasting [16], heart disease classification [17], and so on. However, the convergence speed of GD or GD plus LSE is very slow, and they easily fall into local optimal solutions. In view of the above problems, new techniques based on the ANFIS optimized by EAs have been emerging. For example, [PERSON] et al. proposed the improved ANFIS based on the Harris hawks optimization evolutionary algorithm and demonstrated its effectiveness on the prediction of the longitudinal dispersion coefficient of natural rivers [18]. [PERSON] et al. proposed an ANFIS-PSO method based on an improved particle swarm optimization algorithm and successfully applied it to the evaluation of tool wear [19]. [PERSON] et al. combined the genetic algorithm with the ANFIS to further improve the prediction accuracy of the waterborne disease cholera [20]. In addition, a method of optimizing the ANFIS based on an improved firefly algorithm and the differential evolution optimization algorithm was proposed by [PERSON] [21], which has been proven to be effective in the application of medical disease prediction. [PERSON] et al. used three optimization algorithms (sine-cosine algorithm, particle swarm optimization algorithm, and firefly algorithm) to optimize the ANFIS to improve the prediction accuracy [22]. However, all the above methods only focus on the optimization of FSs and still have challenges in solving high-dimensional data. In order to enable FSs to process high-dimensional data, principal component analysis (PCA) [23] is widely used for dimensionality reduction. [PERSON] et al. combined the ANFIS with PCA to predict the Iranian ionospheric time series, which can shorten the convergence time and obtain the optimal solution [24]. [PERSON] et al. solved the problem of predicting the fracture pressure of defective pipelines more effectively through the combination of PCA and the ANFIS [25].