The Fuzzy Inference System with Least Square Optimization for Time Series Forecasting

Abstract

The rule base on the fuzzy inference system (FIS) has a major role since the output generated by the system is highly dependent on it. The rule base is usually obtained from an expert but in this study proposed the rule base generated based on input-output data pairs with generating rule bases using lookup table scheme, then consequent part of each rule optimized with ordinary least square(OLS), so finally formed rule base from model FIS Takagi-Sugeno orde zero. The exchange rate dataset of EURO to USD is used for the development and validation of the system. In this study, 12 FISs were developed from a combination of linguistic values of n = 3,5,7, 9 with the number of lag (k) assumed to have an effect on output for k = 2,3,5. In training data, values R² ranged between 0.989 and 0.993, MAPE values ranged between 0.381% and 0.473% where the FIS with the combination of n = 9 and k = 5 has the best performance. In the testing data, values R² ranged between 0.203 and 0.7858, MAPE values ranged between 0.5136% and 0.9457% where FIS n = 3 and k = 2 perform best.