Common Decision Trees, Rules, and Tests (Reducts) for Dispersed Decision Tables

In this paper, we assume that a dispersed data is represented by a finite set S of decision tables with equal sets of attributes. We discuss one of the possible ways to the study decision trees common to all tables from the set S: building a decision table for which the set of decision trees coincides with the set of decision trees common to all tables from S. We show when we can build such a decision table and how to build it in a polynomial time. If we have such a table, we can apply to it various decision tree learning algorithms. We extend the considered approach to the study of decision rules and test (reducts) common to all tables from S.