Comparative Analysis of Deterministic and Nondeterministic Decision Trees for Decision Tables from Closed Classes

In this paper, we consider classes of decision tables with many-valued decisions closed under operations of removal of columns, changing of decisions, permutation of columns, and duplication of columns. We study relationships among three parameters of these tables: the complexity of a decision table (if we consider the depth of decision trees, then the complexity of a decision table is the number of columns in it), the minimum complexity of a deterministic decision tree, and the minimum complexity of a nondeterministic decision tree. We consider rough classification of functions characterizing relationships and enumerate all possible seven types of the relationships

APPLICATION OF INFORMATION THEORY TO THE CONSTRUCTION OF EFFICIENT DECISION TREES

This paper treats the problem of conversion of decision tables to decision trees. In most cases, the construction of optimal decision trees is an NP-complete problem and, therefore, a heuristic approach to this problem is necessary. In our heuristic approach, we apply information theoretic concepts to construct efficient decision trees for decision tables which may include “don’t-care” entries. In contrast to most of the existing heuristic algorithms, our algorithm is systematic and has a sound theoretical justification. The algorithm has low design complexity and yet provides us with near-optimal decision trees

Deterministic and Strongly Nondeterministic Decision Trees for Decision Tables from Closed Classes

In this paper, we consider classes of decision tables with 0-1-decisions closed relative to removal of attributes (columns) and changing decisions assigned to rows. For tables from an arbitrary closed class, we study the dependence of the minimum complexity of deterministic decision trees on various parameters of the tables: the minimum complexity of a test, the complexity of the set of attributes attached to columns, and the minimum complexity of a strongly nondeterministic decision tree. We also study the dependence of the minimum complexity of strongly nondeterministic decision trees on the complexity of the set of attributes attached to columns. Note that a strongly nondeterministic decision tree can be interpreted as a set of true decision rules that cover all rows labeled with the decision 1

Comparative Analysis of Deterministic and Nondeterministic Decision Trees for Decision Tables from Closed Classes

In this paper, we consider classes of decision tables with many-valued decisions closed under operations of the removal of columns, the changing of decisions, the permutation of columns, and the duplication of columns. We study relationships among three parameters of these tables: the complexity of a decision table (if we consider the depth of the decision trees, then the complexity of a decision table is the number of columns in it), the minimum complexity of a deterministic decision tree, and the minimum complexity of a nondeterministic decision tree. We consider the rough classification of functions characterizing relationships and enumerate all possible seven types of relationships