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The problem of defining a decision rule which takes into account performance constraints and class-selective rejection is formalized in a general framework. In the proposed formulation, the problem is defined using three kinds of criteria. The first is the cost to be minimized, which defines the objective function, the second are the decision options, determined by the admissible assignment classes or subsets of classes, and the third are the performance constraints. The optimal decision rule within the statistical decision theory framework is obtained by solving the stated optimization problem. Two examples are provided to illustrate the formulation and the decision rule is obtained.