Abstract
Abstract According to the traditional lower-approximation sets, all of the credible rules cannot be induced in the ordered decision system. In order to solve this problem, the concepts of the increasing and decreasing descriptors are proposed, and the relationships between the support sets of these descriptors and the decision class are discussed. Furthermore, the reductions and relative reductions are investigated in terms of the decision classes of these two new descriptors, and the judgment theorems and discernibility functions with respect to these reductions are given. These methods provide a new theory and practical approach, which can generate all optimal credible decision rules from the ordered decision system.
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