Additive similarity measures

  • Authors:

  • Lutz Leischner

  • Affiliations:

  • Fachbereich Mathematik, Darmstadt University of Technology, Schloßgartenstraße, 7, D-64289 Darmstadt, Germany

  • Venue:
  • Discrete Applied Mathematics - Special issue: The 1998 conference on ordinal and symbolic data analysis (OSDA '98)
  • Year:
  • 2003

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Abstract

Following the approach of Tversky's contrast model, similarity measures are introduced as order-preserving maps from specific ordered sets into the non-negative reals. The analysis of this class of functions gives rise to the definition of additive similarity measures that induce a matroid on their domain. An explicit representation of this matroid is given that can be used to directly determine the additive extension of a map from the basis of the matroid. In addition, a criteria is given to check, whether an additive map is a similarity measure or not.