FUZZY RULE-BASED SYSTEMS FOR MULTIVARIATE AND UNIVARIATE HYDROLOGICAL FORECASTING

The fuzzy logic theory and methods provide formal concepts and mathematical techniques from fuzzy sets theory, which can be used in the field of machine learning. These concepts and methods are well suited to handle imprecise and uncertain data commonly collected in the fields of soil and hydrogeological studies. A fuzzy inference system (FIS) is developed for predictions of the groundwater level by means of multivariate mapping of a set of input hydrological and meteorological time series data–precipitation, river flow, and temperature, to the output variable–groundwater level. The time series and correlation analysis showed that the input variables are weakly correlated with the target–groundwater level, and may actually have no predictive power when trying to estimate the target at a later stage using a conventional regression analysis. Two FIS are used for predictions–Mamdani-type and Sugeno-type. The FIS consists of the following steps–a fuzzification of a set of input time series data into fuzzy variables, the development of a set of if-then fuzzy rules, fuzzy interference and defuzzification of predictions into the output time series. Modeling and visualization of predictors were conducted using 26 Gaussian Fuzzy membership functions, the center of gravity defuzzification technique, Zadeh’s implication function, and the Wang-Mendel algorithm in R. Using the diagnostic criteria of accuracy, such as the root mean square error and the symmetric mean absolute percent error, the best accuracy of forward predictions is achieved by a data-driven approach with time steps from 7 to 20 days. A univariate prediction of the water level is performed using the Adaptive Neuro-Fuzzy Inference Systems (ANFIS) technique. It will also be shown how the fuzzy logic concept can be applied for managing groundwater resources in case of using water for pumping or managing a groundwater balance.