Partial covers, reducts and decision rules with weights

In this chapter, we study 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 reducts and decision rules: each conditional attribute has its own weight, and we should minimize the total weight of attributes in partial reduct or decision rule. If weight of each attribute characterizes time complexity of attribute value computation, then we try to minimize total time complexity of computation of attributes from partial reduct or partial decision rule. If weight characterizes a risk of attribute value computation (as in medical or technical diagnosis), then we try to minimize total risk, etc. © 2008 Springer-Verlag Berlin Heidelberg.