A novel measure of compatibility and methods of missing attribute values treatment in decision tables

Based on the fact that the records reflect certain rules included in the decision table, we introduce a novel compatibility measure between any two records for explaining the degree of compatibility of a decision table. This measure is a quite a powerful index that expresses the relations among the records. Combining the index with some commonly used statistical estimates such as mode and mean, we obtain several methods to deal with the missing attribute values in a decision table. In addition, we propose another type of synthetical quantity for a decision table and suggest a way to determine the missing data by optimization methods. The proposed methods have many advantages, especially for a decision table with a large number of attributes and sparse data, or with some logical relations among the condition attribute values of different records.