Abstract

Each realization of a stochastic process is affected by error measurements, meanwhile the prediction of time series only take into account the randomness regarded to the variability of the stochastic process through time. Therefore, the uncertainty of the data is not considered in the conventional modeling and it becomes necessary to design or implement techniques to manage this. In this work, we exhibit the modeling process of a time series based on fuzzy techniques. The implementation of if-then fuzzy rules to model the series can tackle the problem of uncertainty in the input data. The application of fuzzy techniques are performed using the \Takagi-Sugeno-Kang (TSK) to model the time series and to make predictions robustly. The TSK can address the uncertainty by recognizing the local behavior of the process and, moreover, we can interpret the model of the system. Therefore, the if-then fuzzy models have the advantage over conventional nonlinear modeling because the local representation of the process. This local representation allows the description of a nonlinear system using mathematical functions and address the overall complexity underlying the dynamic process. The antecedent of a fuzzy rule divides the input space in local diffuse regions, while the consequent describes the dynamics of these regions. The antecedent of the rule is within certain regions of the input space and the consequent is usually an autoregressive model. Furthermore, the TSK model works as a local predictor because it is associated with a specific region of the input space. Inside these regions, the local predictions describes the dynamic behavior of part of a complete system captured by the antecedent part of the rule[1].The model is applied to forecast the level of concentration of air pollution based on the time series, where this measurements are prone to several sources of noise. Simulations results shows a competitive performance in the mean square error.