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. ."
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