The optimal fuzzy c-regression models (OFCRM) in miles per gallon of cars prediction

Abstract

The fuzzy c-regression models (FCRM) have been known to be used in order to fit models with a certain type of mixed data. In this study, we proposed new optimal FCRM models (OFCRM). In order to obtain the least mean square error (MSE), we proposed modification of wi(x), the backward elimination method and the adjustment of the fuzzifier (w). The wi(x) is found by using the matrix Wi in weighted least-square (WLS) method. The backward elimination method is used in the variable selection in the OFCRM models, whereas the fuzzifier, w is adjusted by putting in various values of w (between 1 and 3). The OFCRM models are tested to the simulated data and the OFCRM models can approximate the given nonlinear system with a higher accuracy. In this study, the fuel consumption of different cars in miles per gallon (MPG) with eight independent variables were predicted using the OFCRM models. It was found that all variables are significant and w= 1.502 is the best fuzzifier value to be used in OFCRM models. The comparison among multiple linear regression (MLR) model, FCRM models and OFCRM models were done to find the best model by using the mean square error (MSE). It was found that the OFCRM models with the lowest MSE (MSE=3.106) tends to be the best model if compared to the MLR model (MSE=8.24) and FCRM models (MSE=7.848). This new technique has been found to have great capabilities and more reliable in predicting the dependent variable.