Multiple Fuzzy Classification Systems

Fuzzy classi¿ers are important tools in exploratory data analysis, which is a vital set of methods used in various engineering, scienti¿c and business applications. Fuzzy classi¿ers use fuzzy rules and do not require assumptions common to statistical classi¿cation. Rough set theory is useful when data sets are incomplete. It de¿nes a formal approximation of crisp sets by providing the lower and the upper approximation of the original set. Systems based on rough sets have natural ability to work on such data and incomplete vectors do not have to be preprocessed before classi¿cation. To achieve better performance than existing machine learning systems, fuzzy classifiers and rough sets can be combined in ensembles. Such ensembles consist of a ¿nite set of learning models, usually weak learners. The present book discusses the three aforementioned ¿elds - fuzzy systems, rough sets and ensemble techniques. As the trained ensemble should represent a single hypothesis, a lot of attention is placed on the possibility to combine fuzzy rules from fuzzy systems being members of classi¿cation ensemble. Furthermore, an emphasis is placed on ensembles that can work on incomplete data, thanks to rough set theory. .