论文信息 - Towards a Conscious Choice of a Fuzzy Similarity Measure: A Qualitative Point of View

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

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.

[1] A. Tversky. Features of Similarity , 1977 .

[2] Bernadette Bouchon-Meunier,et al. Towards general measures of comparison of objects , 1996, Fuzzy Sets Syst..

[3] Bernadette Bouchon-Meunier,et al. Towards a Conscious Choice of a Similarity Measure: A Qualitative Point of View , 2009, ECSQARU.

[4] Marie-Jeanne Lesot,et al. Similarity measures for binary and numerical data: a survey , 2008, Int. J. Knowl. Eng. Soft Data Paradigms.

[5] Maria Rifqi,et al. Mesures de comparaison, typicalite et classification d'objets flous : theorie et pratique , 1996 .

[6] Jaap Van Brakel,et al. Foundations of measurement , 1983 .

[7] Edwina L. Rissland,et al. AI and Similarity , 2006, IEEE Intelligent Systems.

[8] Patrick Suppes,et al. Foundations of Measurement, Vol. II: Geometrical, Threshold, and Probabilistic Representations , 1989 .

[9] V. Batagelj,et al. Comparing resemblance measures , 1995 .

[10] Bernadette Bouchon-Meunier,et al. Similarities in Fuzzy Data Mining: From a Cognitive View to Real-World Applications , 2008, WCCI.

[11] F. B. Baulieu. A classification of presence/absence based dissimilarity coefficients , 1989 .

[12] Bernadette Bouchon-Meunier,et al. Ranking invariance between fuzzy similarity measures applied to image retrieval , 2004, 2004 IEEE International Conference on Fuzzy Systems (IEEE Cat. No.04CH37542).