Abstract
Measuring similarity is an important task in many domains such as psychology, taxonomy, information retrieval, image processing, bioinformatics, and so on. The diversity of domains has led to many different definitions of and methods for determining similarity. Even within fuzzy set theory, how to measure similarity between fuzzy sets presents a wide variety of approaches depending on what characteristic of a fuzzy set is emphasized, for example, set-based, logic-based or geometric-based views of a fuzzy set. First similarity is examined from a psychological viewpoint, and how that perspective might be applicable to fuzzy set similarity measures is explored. Then two fuzzy set similarity measures, one set-based and the other geometric-based, are reviewed, and a comparison is made between the two.
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References
Gregson, R.M.: Psychometrics of Similarity. Academic Press, New York (1975)
Cross, V., Sudkamp, T.: Similarity and Compatibility in Fuzzy Set Theory: Assessment and Applications. Physica-Verlag, New York (2002)
Cross, V.: Ontological similarity. In: Popescu, M., Xu, D. (eds.) Data Mining in Biomedicine Using Ontologies, pp. 23–43. Artech House, Norwood (2009)
Medin, D.L., Goldstone, R.L., Gentner, D.: Respects for similarity. Psychol. Rev. 100, 254–278 (1993)
Tversky, A.: Features of similarity. Psychol. Rev. 84, 327–352 (1977)
Murphy, G.L., Medin, D.L.: The role of theories in conceptual coherence. Psychol. Rev. 92, 289–316 (1985)
Milosavljevic, M.: Comparison purpose and the respects for similarity. In: Slezak, P. (ed.) Proceedings of the Joint International Conference on Cognitive Science with the Australasian Society for Cognitive Science. University of New South Wales, Sydney (2003)
Jaccard, P.: Nouvelles recherches sur la distribution florale. Bull. Soc. Vaud Sci. Nat. 44, 223 (1908)
Sneath, P.H.A., Sokal, R.R.: Numerical Taxonomy. W. H. Freeman and Company, San Francisco (1973)
De Luca, A., Termini, S.: A definition of non-probabilistic entropy in the setting of fuzzy set theory. Inf. Control 20, 301–312 (1972)
Yager, R.R.: On the measure of fuzziness and negation, Part I: membership in the unit interval. Int. J. Gen. Syst. 5, 221–229 (1979)
der Weken, D.V., Nachtegael, M., Kerre, E.E.: Using similarity measures and homogeneity for the comparison of images. Image Vis. Comput. 22, 695–702 (2004)
Zwick, R., Carlstein, E., Budescu, D.: Measures of similarity among fuzzy concepts: a comparative analysis. Int. J. Approx. Reason. 1, 221–242 (1987)
Cross, V., Sudkamp, T.: Geometric compatibility modification. Fuzzy Sets Syst. 84, 283–299 (1996)
Frank, M.J.: On the simultaneous associativity of F(x,y) and x + y − F(x,y). Aequationes Math. 19, 194–226 (1979)
Dubois, D., Prade, H.: A unifying view of comparison indices in a fuzzy set-theoretic framework. In: Yager, R. (ed.) Fuzzy Sets and Possibility Theory: Recent Developments, pp. 3–13. Pergamon Press, New York (1982)
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Cross, V. (2018). Relating Fuzzy Set Similarity Measures. In: Melin, P., Castillo, O., Kacprzyk, J., Reformat, M., Melek, W. (eds) Fuzzy Logic in Intelligent System Design. NAFIPS 2017. Advances in Intelligent Systems and Computing, vol 648. Springer, Cham. https://doi.org/10.1007/978-3-319-67137-6_2
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DOI: https://doi.org/10.1007/978-3-319-67137-6_2
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