Flexible Evolving Fuzzy Inference Systems from Data Streams (FLEXFIS++)

Data streams are usually characterized by an ordered sequence of samples recorded and loaded on-line with a certain frequency arriving continuously over time. Extracting models from such type of data within a reasonable on-line computational performance can be only achieved by a training procedure which is able to incrementally build up the models, ideally in a single-pass fashion (not using any prior samples). This chapter deals with data-driven design of fuzzy systems which are able to handle sample-wise loaded data within a streaming context. These are called Flexible Evolving Fuzzy Inference Systems (FLEXFIS) as they may permanently change their structures and parameters with newly recorded data, achieving maximal flexibility according to new operating conditions, dynamic system behaviors or exceptional occurrences. We are explaining how to deal with parameter adaptation and structure evolution on demand for regression as well as classification problems. In the second part of the chapter, several key extensions of the FLEXFIS family will be described (leading to the FLEXFIS++ and FLEXFIS-Class++ variants), including concepts for on-line rule merging, dealing with drifts and reducing the curse of dimensionality as well as interpretability considerations and reliability in model predictions. Successful applications of the FLEXFIS family are summarized in a separate section. An extensive evaluation of the proposed methods and techniques will be demonstrated in a separate chapter (Chapter 14), when dealing with the application of flexible fuzzy systems in on-line quality control systems.