Cars are regarded as an indispensable means of transportation in Taiwan. Several studies have indicated that the automotive industry has witnessed remarkable advances and that the market of used cars has rapidly expanded. In this study, a price prediction system for used BMW cars was developed. Nine parameters of used cars, including their model, registration year, and transmission style, were analyzed. The data obtained were then divided into three subsets. The first subset was used to compare the results of each algorithm. The predicted values produced by the two algorithms with the most satisfactory results were used as the input of a fully connected neural network. The second subset was used with an optimization algorithm to modify the number of hidden layers in a fully connected neural network and modify the low, medium, and high parameters of the membership function (MF) to achieve model optimization. Finally, the third subset was used for the validation set during the prediction process. These three subsets were divided using k-fold cross-validation to avoid overfitting and selection bias. In conclusion, in this study, a model combining two optimal algorithms (i.e., random forest and k-nearest neighbors) with several optimization algorithms (i.e., gray wolf optimizer, multilayer perceptron, and MF) was successfully established. The prediction results obtained indicated a mean square error of 0.0978, a root-mean-square error of 0.3128, a mean absolute error of 0.1903, and a coefficient of determination of 0.9249.
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