Towards a Conscious Choice of a Similarity Measure: A Qualitative Point of View

Authors:
Bernadette Bouchon-Meunier;Giulianella Coletti;Marie-Jeanne Lesot;Maria Rifqi
Affiliations:
Université Pierre et Marie Curie - Paris 6, CNRS UMR 7606, LIP6, Paris, France F-75016;Dipartimento Matematica e Informatica, Università di Perugia, Perugia, Italy 06123;Université Pierre et Marie Curie - Paris 6, CNRS UMR 7606, LIP6, Paris, France F-75016;Université Pierre et Marie Curie - Paris 6, CNRS UMR 7606, LIP6, Paris, France F-75016
Venue:
ECSQARU '09 Proceedings of the 10th European Conference on Symbolic and Quantitative Approaches to Reasoning with Uncertainty
Year:
2009

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Abstract

In many applications, such as case based reasoning, data mining or analogical reasoning, the choice of a particular measure of similarity is crucial. In this paper, we propose to study similarity measures from the point of view of the ordering relation they induce on object pairs. Using a classic method in measurement theory, introduced by Tversky, we establish necessary and sufficient conditions for the existence of a specific numerical measure, or a class of measures, to represent a given ordering relation, depending on the axioms this relation satisfies. The interest is particularly focused on different conditions of independence.