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An Optimum Class-Rejective Decision Rule and Its Evaluation

Decision-making systems intend to copy human reasoning which often consists in eliminating highly non probable situations (e.g. diseases, suspects) rather than selecting the most reliable ones. In this paper, we present the concept of class-rejective rules for pattern recognition. Contrary to usual reject option schemes where classes are selected when they may correspond to the true class of the input pattern, it allows to discard classes that can not be the true one. Optimality of the rule is proven and an upper-bound for the error probability is given. We also propose a criterion to evaluate such class-rejective rules. Classification results on artificial and real datasets are provided.