This book explores, within the framework of rough set theory, the complexity of decision trees and decision rule systems and the relationships between them for problems over information systems, for decision tables from closed classes, and for problems involving formal languages. Decision trees and systems of decision rules are widely used as means of representing knowledge, as classifiers that predict decisions for new objects, as well as algorithms for solving various problems of fault diagnosis, combinatorial optimization, etc. Decision trees and systems of decision rules are among the most interpretable models of knowledge representation and classification. Investigating the relationships between these two models is an important task in computer science.

The possibilities of transforming decision rule systems into decision trees are being studied in detail. The results are useful for researchers using decision trees and decision rule systems in data analysis, especially in rough set theory, logical analysis of data, and test theory. This book is also used to create courses for graduate students.

Inhalt

Introduction.- Problems Over Information Systems.- Comparative Analysis of Deterministic and Nondeterministic Decision Tree Complexity Global Approach.- Comparative Analysis of Deterministic and Nondeterministic Decision Tree Complexity Local Approach.- Time and Space Complexity of Deterministic and Nondeterministic Decision Trees Global Approach.- Time and Space Complexity of Deterministic and Nondeterministic Decision Trees Local Approach.- Decision Tables from Closed Classes.- Comparative Analysis of Deterministic and Nondeterministic Decision Trees for Decision Tables from Closed Classes.- Complexity of Deterministic and Nondeterministic Decision Trees for Decision Tables with Many-valued Decisions from Closed Classes.- Complexity of Deterministic and Nondeterministic Decision Trees for Conventional Decision Tables from Closed Classes.- Complexity of Deterministic and Strongly Nondeterministic Decision Trees for Decision Tables with 0 1 Decisions from Closed Classes.- Recognition and Membership Problems for Formal Languages.- Decision Trees for Binary Subword closed Languages.- Transforming Decision Rule Systems into Deterministic Decision Trees.- Bounds on Depth of Decision Trees Derived from Decision Rule Systems.- Construction of Decision Trees and Acyclic Decision Graphs from Decision Rule Systems.