Abstract
This paper describes LSE method for improving Takagi-Sugeno neuro-fuzzy model for a multi-input and multi-output system using a set of data (Mackey-Glass chaotic time series). The performance of the generated model is verified using certain set of validation / test data. The LSE method is used to compute the consequent parameters of Takagi-Sugeno neuro-fuzzy model while mean and variance of Gaussian Membership Functions are initially set at certain values and will be updated using Back Propagation Algorithm. The simulation using Matlab shows that the developed neuro-fuzzy model is capable of forecasting the future values of the chaotic time series and adaptively reduces the amount of error during its training and validation.
Highlights
When considering fuzzy logic for analyzing and solving certain problem in engineering which requires computational intelligence, practically ones choose between Mamdani model and Takagi-Sugeno model
Takagi-Sugeno model is preferred in the case of data-based fuzzy modeling [1, 2, 3] as well as forecasting time series data where in many cases it can be seen as system with locally linear model
Another advantage is that the inference formula of the Takagi-Sugeno model is only two-step procedure, based on a weighted average defuzzifier, whereas Mamdani type of fuzzy model basically consists of four steps [4, 5]
Summary
When considering fuzzy logic for analyzing and solving certain problem in engineering which requires computational intelligence, practically ones choose between Mamdani model and Takagi-Sugeno model Another model could be used as well. Takagi-Sugeno model is preferred in the case of data-based (or numerically-data-driven) fuzzy modeling [1, 2, 3] as well as forecasting time series data where in many cases it can be seen as system with locally linear model. We explain the importance of MIMO Takagi-Sugeno Neuro-Fuzzy implementation for time series forecasting and treatment procedure of data, in this case we use Mackey-Glass chaotic time series. We consider short-term forecasting as the implementation case of MIMO Takagi-Sugeno Neuro-Fuzzy for chaotic time series.
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