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

  • Authors:
  • Laurent Mascarilla;Michel Berthier;Carl Frélicot

  • Affiliations:
  • Lab. Mathématiques, Images et Applications - Université de La Rochelle, Avenue Michel Crépeau, 17042 La Rochelle Cedex 1, France;Lab. Mathématiques, Images et Applications - Université de La Rochelle, Avenue Michel Crépeau, 17042 La Rochelle Cedex 1, France;Lab. Mathématiques, Images et Applications - Université de La Rochelle, Avenue Michel Crépeau, 17042 La Rochelle Cedex 1, France

  • Venue:
  • Fuzzy Sets and Systems
  • Year:
  • 2008

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Abstract

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.