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At the beginning of this chapter a small introduction regarding mathematical modelling in general will be given, including first principle and knowledge-based models. Then, we outline a motivation for the usage of a data-driven model design in industrial systems and the necessity for an evolving component therein, especially in on-line applications and in case of huge data bases. Hereby, we will describe concrete requirements and mention application examples, where on-line evolving models serve as key components for increasing predictive accuracy and product quality. After explaining why fuzzy systems provide a potential model architecture for data-driven modelling tasks, we define several types of fuzzy systems mathematically and formulate the goals of an incremental learning algorithm for evolving fuzzy systems from a mathematical and machine learning point of view. Hereby, we also highlight which components in fuzzy systems have to be adapted and evolved in order to guarantee stable models with high predictive power. The chapter is concluded by outlining a summary of the content in this book.
KeywordsFuzzy System Incremental Learning Consequent Part Antecedent Part Incremental Learning Algorithm
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