@inproceedings{85413a4e0a4c4c11a3571ce9a474358d,
title = "Deterministic and Nondeterministic Decision Trees for Decision Tables with Many-Valued Decisions from Closed Classes",
abstract = "Decision rules and decision trees are studied intensively in rough set theory. The following questions seem to be important for this theory: relations between decision trees and decision rule systems, and dependence of the complexity of decision trees and decision rule systems on the complexity of the set of attributes attached to columns of the decision table. In this paper, instead of decision rule systems we study nondeterministic decision trees that can be considered as representations of decision rule systems. We consider classes of decision tables with many-valued decisions (multi-label decision tables) closed relative to removal of attributes (columns) and changing sets of decisions assigned to rows. For tables from an arbitrary closed class, we study functions that characterize the dependence in the worst case of the minimum complexity of deterministic and nondeterministic decision trees on the complexity of the set of attributes attached to columns. We enumerate all types of behavior of these functions. We also study the dependence in the worst case of the minimum complexity of deterministic decision trees on the minimum complexity of nondeterministic decision trees. This study leads to understanding of the nontrivial relationships between deterministic decision trees and systems of decision rules represented by nondeterministic decision trees.",
keywords = "Closed classes of decision tables, Decision tables with many-valued decisions, Deterministic decision trees, Nondeterministic decision trees",
author = "Azimkhon Ostonov and Mikhail Moshkov",
note = "Publisher Copyright: {\textcopyright} The Author(s), under exclusive license to Springer Nature Switzerland AG 2023.; International Joint Conference on Rough Sets, IJCRS 2023 ; Conference date: 05-10-2023 Through 08-10-2023",
year = "2023",
doi = "10.1007/978-3-031-50959-9_7",
language = "English (US)",
isbn = "9783031509582",
series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",
publisher = "Springer Science and Business Media Deutschland GmbH",
pages = "89--104",
editor = "Andrea Campagner and {Urs Lenz}, Oliver and Shuyin Xia and Dominik {\'S}l{\c e}zak and Jaros{\l}aw W{\c a}s and JingTao Yao",
booktitle = "Rough Sets - International Joint Conference, IJCRS 2023, Proceedings",
address = "Germany",
}