## 3 Results and Discussion  
The main focus of this paper is to establish a reliable and robust model based on the ability of different types of hybrid ANFIS approaches to predict the \(Ss\) prediction of HSC. The challenges of the mathematical and empirical relations establishing the appropriate relationship between the \(Ss\) and HSC properties highlight the intervention of soft computing aids. However, establishing the internal mechanism between the related predictors towards the \(Ss\) of HSC has a substantial motive for investigation and examination. Furthermore, robust and reliable models can always construct a precise intelligence-optimizing technology in the field of structural engineering. Thus, the proposal of a new hybrid intelligence model can enhance the reliable contribution to the structure design along with various reinforcement concrete engineering perspectives. The proposed hybrid intelligence models and the standalone ANFIS models were evaluated based on various performance metrics and graphical presentations, including heat map, scatterplot, boxplot, and Taylor diagrams over the training and testing phase for modeling \(Ss\) of HSC. Besides, the new ANFIS models were assessed based on the hybridization algorithms, variables, and data uncertainty. The performance of classical ANFIS is assessed in both training and testing period for different input combination models (Model 1-18) using RMSE, MAE, LMI, CC, WI, and SRMSE (Table 2). The input combination of Model 8 (Incorporated: \(a\), \(a_{g}\), \(\ell\), and \(\rho\)) appeared to be the most appropriate choice for generating good prediction results over the training and testing stages. The acquired magnitudes of assessing metrics in training and testing are: ANFIS (\(RMSE=0.263\), \(0.314\); \(MAE=0.198\), \(0.224\); \(LMI=0.675\), \(0.640\); \(CC=0.936\), \(0.920\); \(WI=0.966\), \(0.957\); \(SRMSE=15.011\), \(19.584\)). The hybrid ANFIS-ACO model produced the lowest magnitudes of _RMSE_, _MAE_, _SRMSE_, and highest _LMI_, _CC_, and _WI_ values (\(RMSE\approx 0.377\), \(0.399\), \(MAE\approx 0.282\), \(0.289\), _SRMSE_\(\approx 21.563\), \(24.912\)) and (_LMI_\(\approx 0.537\), \(0.536\), \(CC\approx 0.863\), \(0.870\), \(WI\approx 0.921\), \(0.918\)) for both training and testing stages, respectively. The best prediction was achieved for the input combination of Model-16 (incorporated: \(d\), \(\rho\), \(a\)/\(d\), \(fc\)). These metrics for other input combination models using ANFIS-ACO can be seen in Table 3. Likewise, the preciseness of ANFIS-ACO with input combination in Model-16 is considerably good for predicting _Ss_ (Table 3). Tables 4 and 5 present the statistical performance accuracy of ANFIS-DE and ANFIS-GA models. The ANFIS-DE with input combination in Model-13 (incorporated: \(d\), \(\rho\), \(a\)/\(d\), \(a\)/\(d\), \(fc\)) performed the reasonable prediction for the _Ss_ by obtaining (\(RMSE=0.375\), \(0.398\); \(MAE=0.281\), \(0.291\); \(LMI=0.538\), \(0.533\); \(CC=0.865\), \(0.870\); \(WI=0.922\), \(0.919\); \(SRMSE=21.417\), \(24.838\)) for both training and testing phases. However, ANFIS-GA with Model-16 (incorporated: \(d\), \(\rho\), \(a\)/\(d\), \(fc\)) achieved highest level of accuracy in accordance the statistical metrics (\(RMSE=0.286\), \(0.296\); \(MAE=0.224\), \(0.243\); \(LMI=0.632\), \(0.610\); \(CC=0.924\), \(0.930\); \(WI=0.959\), \(0.962\); \(SRMSE=16.358\), \(18.477\)) (Table 5).