## 3 Proposed Model Using ANFIS  
Several researchers [1, 7, 8, 9, 10, 11, 12, 13] have investigated the effects of the concrete compressive strengths of the column and the slab (\(f^{\prime}_{cc}\) and \(f^{\prime}_{cj}\)), the column width (\(c\)), and the slab thickness (\(h\)) on the effective compressive strength of the column (\(f^{\prime}_{cc}\)). According to the test results conducted by [PERSON] and [PERSON] [9] and [PERSON] [12], the effective compressive strength of the column (\(f^{\prime}_{cc}\)) increases as the aspect ratio of slab thickness to column width (\(h/c\)) decreases. Based on these results, the concrete compressive strength of the column and slab (\(f^{\prime}_{cc}\) and \(f^{\prime}_{cj}\)), and the aspect ratio of slab thickness to column width (\(h/c\)) were chosen as the input variables for estimating the effective compressive strength of the column (\(f^{\prime}_{cc}\)). In addition, a total of 75 test results were collected from the existing literature, as shown in Table 1[2, 26, 27, 7, 9, 12, 2]. Although the authors have put all their efforts in to collect all the test results available up to date, it should be noted that the test data are not yet sufficient enough. Among the collected test specimens, 50 specimens were randomly sampled and used in the training of the ANFIS algorithm, and the remaining 25 specimens were used for verification. As shown in Figure 2, the bell-shaped function was applied as the shape of the fuzzy set, and the membership function of the bell-shaped fuzzy set is calculated as follows:  
\[\text{membership function}=\frac{1}{1+\left|\frac{x-x_{t}}{x_{w}}\right|^{ 2x_{t}}} \tag{2}\]  
Figure 1: Concept of fuzzy inference and ANFIS structure. where \(x\) is the input variable, and \(x_{c}\), \(x_{w}\) and \(x_{q}\) are the shape factors of the fuzzy set, which determine the center, width, and slope parameters of the fuzzy set, respectively. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Researcher** & **Number of Specimens** & \(f^{\prime}_{ce}\) (**MPa**) & \(f^{\prime}_{ej}\) (**MPa**) & \(f^{\prime}_{ce}\) (**MPa**) * & _hLc_ \\ \hline [PERSON] et al. [2] & 1 & 88.33 & 46.89 & 53.3 & 0.6 \\ [PERSON] et al. [5] & 22 & 15.8–46.9 & 8.8–24.8 & 12.8–29 & 0.6 \\ [PERSON] and [PERSON] [7] & 6 & 79.3–97.9 & 15.9–45.5 & 15.8–46.9 & 0.5–0.7 \\ [PERSON] and [PERSON] [9] & 3 & 77.4–83.9 & 17.5–28.2 & 31.7–33.7 & 0.3–0.8 \\ [PERSON] and [PERSON] [12] & 41 & 38.6–50.8 & 6.9–39.2 & 8.6–43.6 & 0.2–3 \\ [PERSON] et al. [26] & 1 & 84 & 29 & 42.3 & 0.6 \\ [PERSON] et al. [27] & 1 & 80.7 & 30 & 43.8 & 0.7 \\ \hline \hline \end{tabular}  
* Note: \(f^{\prime}_{ce}=\frac{P_{tot}-f^{\prime}_{ej}}{\pi\left(A_{g}-A_{h}\right)}\) where \(P_{tot}\) is the axial force measured in the experiment, \(\alpha\) is 0.85 in ACI 318 and 0.85–0.0015 \(f^{\prime}_{e}\) in CAA23.3, \(f^{\prime}_{ej}\) is the compressive strength of the concrete, \(A_{g}\) is the gross sectional area of the column, and \(A_{s}\) and \(f_{y}\) are the sectional area and yield strength of the longitudinal reinforcement in the column, respectively.  
\end{table} 
Table 1: Summary of collected test specimens. Figure 2: Comparison of membership functions before and after training. For the fuzzy theory, including ANFIS, the accuracy of the results greatly depends on the configuration of the fuzzy set. Therefore, it is of utmost importance to configure the fuzzy set appropriately. In the general fuzzy theory, the fuzzy set is configured by referring to the existing codes and experts' consensus. However, in the ANFIS, the initial fuzzy set is assumed based on the collected data, and the optimized fuzzy set is then configured by means of repetitive training. In this study, the shape factors of the initial fuzzy set were assumed, using the K-means clustering technique proposed by [PERSON] [28]. Figure 2 compares the initial membership function and the final membership function determined after the ANFIS training, which are denoted by a dotted line and a solid line, respectively.