Minimal inhibitory association rules for almost all k -valued information systems

There are three approaches to use inhibitory rules in classifiers: (i) lazy algorithms based on an information about the set of all inhibitory rules, (ii) standard classifiers based on a subset of inhibitory rules constructed by a heuristic, and (iii) standard classifiers based on the set of all minimal (irreducible) inhibitory rules. The aim of this chapter is to show that the last approach is not feasible (from computational complexity point of view). We restrict our considerations to the class of k-valued information systems, i.e., information systems with attributes having values from {0,..., k-1}, where k >2. Note that the case k=2 was considered earlier in [51].