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In this paper, we present a pretopological approach for pattern classification with reject options. The pretopological approach, based on growing -neighborhoods, already has proved its efficiency in reducing computation time and storage requirements compared to a k-Nearest Neighbors approach. By including ambiguity and distance reject options, we give to such an approach more adaptability to real classification problems for which classes generally are not clearly separable and/or not completely known. In order to control both types of rejection, the proposed classifier needs a unique parameter to be fixed whereas two parameters generally are necessary (one for each reject type). We also have observed that the behavior of the classifier (depending of the parameter value) with respect to both kinds of rejection is similar to the behavior of well-known rejection-based classifiers proposed so far in the literature.

A pretopological approach for pattern classification with reject options