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 sufficient conditions for the existence of a class of numerical similarity measures, to represent a given ordering relation, depending on the axioms this relation satisfies.
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Bouchon-Meunier, B., Coletti, G., Lesot, MJ., Rifqi, M. (2010). Towards a Conscious Choice of a Fuzzy Similarity Measure: A Qualitative Point of View. In: Hüllermeier, E., Kruse, R., Hoffmann, F. (eds) Computational Intelligence for Knowledge-Based Systems Design. IPMU 2010. Lecture Notes in Computer Science(), vol 6178. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-14049-5_1
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DOI: https://doi.org/10.1007/978-3-642-14049-5_1
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