Towards a conscious choice of a similarity measure: a qualitative point of view

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.
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Bernadette Bouchon-Meunier, Giulianella Coletti, Marie-Jeanne Lesot, Maria Rifqi. Towards a conscious choice of a similarity measure: a qualitative point of view. 10th European Conference on Symbolic and Quantitative Approaches to Reasoning with Uncertainty (ECSQARU 2009), Jul 2009, Verona, Italy. pp.542-553, ⟨10.1007/978-3-642-02906-6_47⟩. ⟨hal-01072117⟩

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