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This book explores decision trees and decision rule systems, rules and reducts, examines relationships among these objects and reviews the design of algorithms for construction of trees, rules and reducts. Includes carefully selected illustrative proofs.

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Decision trees and decision rule systems are widely used in different applications
as algorithms for problem solving, as predictors, and as a way for
knowledge representation. Reducts play key role in the problem of attribute
(feature) selection. The aims of this book are (i) the consideration of the sets
of decision trees, rules and reducts; (ii) study of relationships among these
objects; (iii) design of algorithms for construction of trees, rules and reducts;
and (iv) obtaining bounds on their complexity. Applications for supervised
machine learning, discrete optimization, analysis of acyclic programs, fault
diagnosis, and pattern recognition are considered also. This is a mixture of
research monograph and lecture notes. It contains many unpublished results.
However, proofs are carefully selected to be understandable for students.
The results considered in this book can be useful for researchers in machine
learning, data mining and knowledge discovery, especially for those who are
working in rough set theory, test theory and logical analysis of data. The book
can be used in the creation of courses for graduate students.

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Part I Tools.- Part II Applications.

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