Fuzzy linear regression based on a hybrid of fuzzy C-means and the fuzzy inference system for predicting serum iron levels in patients with chronic kidney disease

Multiple regression has been proven to be a reliable method for solving prediction problems that require many independent variables. The biggest challenge in multiple regression is that the number of samples given must be sufficient based on the number of independent variables. In some cases, it may not be possible to eliminate the independent variables via feature selection. This study aims to build a multiple linear regression problem-solving model using Sugeno's fuzzy inference system (FIS) approach. The main contribution of this study is to provide an alternative model for performing linear regression, which has quite a lot of independent variables but not too many datasets. The case that was resolved was the prediction of serum iron (SI) based on nine independent variables of hematology measurement results. The proposed FIS model uses Fuzzy C-Means (FCM) clustering to produce fuzzy sets and fuzzy rules. The Gauss membership function is used as the membership function in each fuzzy set. The output of the fuzzy rules is a linear equation based on the Sugeno Order 1 fuzzy inference method. To test the performance of the model, a comparison of the mean square error (MSE) output of the system with classical multiple linear regression (CMLR) and backpropagation neural networks (BNNs) was performed. In nine scenarios, comparisons were made. The results showed that FIS had the best performance in each scenario. In training data, FIS had the best performance with an MSE of 0.0148, followed by CMLR and BNN with MSEs of 0.0180 and 0.0285, respectively. Whereas in data testing, FIS had the best performance with an MSE of 0.0239, followed by BNN and CMLR with MSEs of 0.0246 and 0.0255, respectively. Even in scenarios where there is little training data, FIS still shows good performance, with MSEs of 0.0219 and 0.0402 on training and testing data, respectively.