Fuzzy modelling with linguistic equations

Abstract

<div lang="en" class="abs"><p class="abs_header">Abstract</p><p>In this report, different types of fuzzy models have been developed from linguistic equations models. Different shapes of membership functions were compared: triangular and trapezoidal membership functions as well as their non-linear modifications were used. ANFIS (adaptive neuro-fuzzy inference system) method for Takagi-Sugeno type models was used and clustering for Singleton fuzzy models. Also the different number of singleton values in singleton fuzzy models and by using fuzzy relations different amount of rules was compared. The data-based approaches are based on data from the Cooking Liquor Analyser CLA 2000. Linguistic equations (LE) work well for this data. For the test data, the performance of the real-valued LE model was the best although a better fitting accuracy with training data was obtained by constructing Takagi-Sugeno (TS) fuzzy models with the ANFIS method. There are also overfitting problems with the TS models. Easy configuration and robustness are the main benefits of the LE models. The fitting performance must be compared to the number of modelling parameters. </p></div>