A k-order fuzzy OR operator for pattern classification with k-order ambiguity rejection

In pattern recognition, the membership of an object to classes is often measured by labels. This article mainly deals with the mathematical foundations of labels combination operators, built on t-norms, that extend previous ambiguity measures of objects by dealing not only with two classes ambiguities but also with k classes, k lying between 1 and the number of classes c. Mathematical properties of this family of combination operators are established and a weighted extension is proposed, allowing to give more or less importance to a given class. A classifier with reject options built on the proposed measure is presented and applied on synthetic data. A critical analysis of the results led to derivate some new operators by aggregating previous measures. A modified classifier is proposed and applied to synthetic data as well as to standard real data.