Prediction of chaotic time-series by using the multi-stage fuzzy inference systems and its applications to the analysis of operational flexibility

This paper deals with the prediction of chaotic time series by using the multi-stage fuzzy inference system and its application to the analysis of operating flexibility. Multi-national corporation obtained by shifting manufacturing plants located in different countries is denoted as operating flexibility. Even though the operating flexibility is optimized by the stochastic dynamic programming under the known process of exchange rate, it is usually hard to explicitly predict the change. Therefore, the value of operating flexibility depends on the prediction of time series. Then, we utilize the prediction of exchange rate by using the multi-stage fuzzy inference system. Since we divide the fuzzy inference system and related input variables into several stages, the number of rules included in multi-stage fuzzy inference systems is remarkably smaller compared to conventional fuzzy inference systems. The weight included in inference rules is optimized by the backpropagation algorithm. We also propose a method to optimize the shape of membership function and the appropriate selection of input variables based upon the genetic algorithm (GA). The method is applied to the approximation of typical multi-dimensional chaotic dynamics. The simulation study for multi-dimentional chaotic dynamics shows that the inference system gives a better prediction. The prediction is then applied to estimate the exchange rates by using input variables consisting of economic indicators as well as the exchange rates. The result shows a better performance of the multi-stage fuzzy inference system than when conventional methods are used. Then, we can find effective operating flexibility for shifting the manufacturing plants depending on the predicted exchange rate.