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

Abstract : In this paper, we propose to study similarity measures among fuzzy subsets from the point of view of the ranking relation they induce on object pairs. Using a classic method in measurement theory, introduced by Tversky, we establish necessary and su cient conditions for the existence of a class of numerical similarity measures, to represent a given ordering relation, depending on the axioms this relation satis es.
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Bernadette Bouchon-Meunier, Giulianella Coletti, Marie-Jeanne Lesot, Maria Rifqi. Towards a conscious choice of a fuzzy similarity measure: a qualitative point of view. International conference on Information Processing and Management of Uncertainty in knowledge-based systems, IPMU 2010, Jun 2010, Dortmund, Germany. pp.1-10, ⟨10.1007/978-3-642-14049-5_1⟩. ⟨hal-01072127⟩

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