A new framework for missing data estimation and reconstruction based on the geographical input information, data mining, and multi-criteria decision-making; theory and application in missing groundwater data of Damghan Plain, Iran

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In the present study, a new framework is developed based on the geographical data (GD), data mining techniques (DI), and Hesitant fuzzy-multicriteria decision-making methods (HF-MCDA) for modeling groundwater table (GWT) missing data in Damghan plain. The GD is used as inputs in the presented approach, and available GWT is used as output. The different DI, including artificial neural network (ANN), tree model M5 (M5), multivariate adaptive regression spline (MARS), least-square support vector machine (LSSVM), random forest (RF), and extreme learning machine (ELM), are employed for establishing a relation between GD and GWT and estimating missing GWT. However, there is this challenge that one of the DI is better because there are different criteria for selecting the best DI, including error criteria, uncertainty, and computation time. Moreover, there is hesitation about the choice of weight criteria. In this condition, HF-MCDA is a practical choice. According to the results, M5 (by values of 5.485 m, 10.811 m, and 0.998 for MAE, RMSE, and R2, respectively) and LSSVM (by values of 3.043 m, 17.005 m, and 0.997 for MAE, RMSE, and R2, respectively) have accurate results than other investigated DI. In contrast, ELM has the worst results in terms of accuracy. M5 and RF have the best and worst performance based on the time computation term. The results of bootstrap uncertainty show that LSSVM has minimum uncertainty (by the value of 1.349 m for d_factor), and ELM has maximum uncertainty (by the value of 1.570 m for d_factor). Finally, according to the results of HF-MCDA, M5, LSSVM has first and the second rank with a closed score. Besides, the MARS algorithm is placed B in the third rank with a slight difference from M5 and LSSVM. Based on the high and closed scores of M5, LSSVM, and MARS, these methods can be used to find missing GWT data.