On minimal inhibitory rules for almost all k-valued information systems

The minimal inhibitory rules for information systems can be used for construction of classifiers. We show that almost all information systems from a certain large class of information systems have relatively short minimal inhibitory rules. However, the number of such rules is not polynomial in the number of attributes and the number of objects. This class consists of all k-valued information systems, k ≥ 2, with the number of objects polynomial in the number of attributes. Hence, for efficient construction of classifiers some filtration techniques in rule generation are necessary. Another way is to work with lazy classification algorithms based on inhibitory rules.