## 1 Introduction
Furthermore, the authors considered one or two hidden layers, as, if more are used, this can lead to a high prediction error. Although ANN is more efficient and accurate than mathematical models, numerous research works have highlighted ANN's limitations, such as becoming trapped in local vertices and showing constraints to cross-peaks in the error function range. [PERSON] et al. [17] pointed out that ANN has limitations in geotechnical domains. The inability to extract information from trained neural networks and forecast outside the range of training data are two of these constraints. Several researchers have proposed ANN hybridization with other optimization models to enhance the computing ability of ANN [18]. The adaptive network-based fuzzy inference system (ANFIS) is a neural network based on the Takagi-Sugeno fuzzy inference system. It offers the possibility to harness the benefits of pairing neural networks and fuzzy logic principles in a single structure, since it incorporates both. Its inference system comprises a collection of fuzzy IF-THEN rules with the capacity to approximate nonlinear equations through learning and forecasting disordered time series. Various types of fuzzy inference systems have been identified in the literature. They may be divided into three types, described in detail by [PERSON] [19]. Figure 3 depicts a two-input type 3 fuzzy inference system construction with five layers separated. Input variables are represented by x and y; layer 1 has square nodes, which are labeled A for input x and B for input y; layer 2 has circled nodes, which are labeled \(\Pi\); layer 3 has circled nodes, which are labeled N; layer 4 has square nodes, which are labeled 1-9; and layer 5, the sum of all incoming signals, has a circled node that is labeled \(\Sigma\). Figure 3: Two-input type 3 fuzzy inference. Many researchers have studied the prediction of surface roughness using the ANFIS model with satisfactory results. The ANFIS model has been used as a stand-alone or hybrid in CNC turning operations to forecast surface roughness [20; 21; 22]. [PERSON], [PERSON], and [PERSON] [23] employed ANFIS modeling to predict the surface roughness by using the Wire Electric Discharge Machining (WEDM) manufacturing method to machine the aluminum alloy AA6063. They considered four input machining variables: pulse on time (Ton), pulse off time (Toff), peak current (Ip), and servo voltage (Vs). Utilizing a scanning electron microscope (SEM), the surface integrity appearance was examined. Five alternative Ton, Toff, Ip, and Vs input parameters were used to machine the AA6063. The ANFIS was created to outperform the trapezoidal, gbell, and Gaussian membership functions with the lowest performance characteristic of the triangle membership function. [PERSON] [24] collected data using a CNC lathe machine by turning a stork of 50 aluminum parts with varying independent parameters: the speed, the feed, and the depth of cut. Then, the surface roughness of each part was experimentally measured. Fifty data were collected, from which 40 data were used to train the ANFIS model on the Matlab interface, while 10 data were used for testing by weighing up the performance of the bell and triangular membership functions. Furthermore, advanced regression analysis was employed in a python environment to validate the predicted outcome. As result, the ANFIS model using a bell-shaped membership function outperformed the others, with higher accuracy and a smaller error. Unlike the ANN model, the hidden layers are decided by an FIS in the ANFIS model, thus solving the well-known problem of finding the hidden layer in the ANN system to increase its prediction abilities. Despite the advantages of the ANFIS model, it has some drawbacks. [PERSON] et al. [25] pointed out that the burden of complexity and computing costs are two drawbacks of ANFIS that prevent it from being used in issues with extensive inputs.