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

Laurent Mascarilla (1) , Michel Berthier (1) , Carl Frelicot (1)

1 MIA - Mathématiques, Image et Applications - EA 3165

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 2 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.

Mots clés: triangular norms; ambiguity measure; classification; reject options

Domaines: Intelligence artificielle [cs.AI]

Laurent Mascarilla, Michel Berthier, Carl Frelicot. A k-order fuzzy OR operator for pattern classification with k-order ambiguity rejection. Fuzzy Sets and Systems, 2008, 159 (15), pp.2011-2029. ⟨10.1016/j.fss.2008.02.019⟩. ⟨hal-00289367⟩