An Experimental Comparison of Three Probabilistic Approximations Used for Rule Induction
In this paper we present results of experiments on 166 incomplete data sets using three probabilistic approximations: lower, middle, and upper. Two interpretations of missing attribute values were used: lost and "do not care" conditions. Our main objective was to select the best combination of an approximation and a missing attribute interpretation. We conclude that the best approach depends on the data set. The additional objective of our research was to study the average number of distinct probabilities associated with characteristic sets for all concepts of the data set. This number is much larger for data sets with "do not care" conditions than with data sets with lost values. Therefore, for data sets with "do not care" conditions the number of probabilistic approximations is also larger.
incomplete data lower characteristic sets singleton subset and concept approximations middle and upper approximations