Partial covers and inhibitory decision rules with weights

In this chapter, we consider the case, where each subset, used for covering, has its own weight, and we should minimize the total weight of subsets in partial cover. The same situation is with partial inhibitory decision rules: each conditional attribute has its own weight, and we should minimize the total weight of attributes occurring in partial inhibitory decision rule. If weights of attributes characterize time complexity of attribute value computation, then we try to minimize total time complexity of computation of attributes from partial inhibitory decision rule. If weights characterize a risk of attribute value computation (as in medical or technical diagnosis), then we try to minimize total risk, etc.