Imprecision and Structure in Modelling Subjective Similarity

  • Thomas Sudkamp
Part of the CISM International Centre for Mechanical Sciences book series (CISM, volume 504)


Similarity measures based on feature matching have been designed for modelling subjective similarity judgements. In this paper, the taxonomic presence-absence feature representation is extended to assess the similarity of objects whose attributes are described by partial satisfaction of predicates or by fuzzy sets. The principle of minimum specificity is used to obtain possibilistic bounds on the combination of similarity assessments. A priority hierarchy and bipolarity are incorporated into similarity measurement to utilize inter-attribute relationships in modelling similarity judgements.


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  1. S. Armstrong, L. Gleitman, and H. Gleitman. What some concepts might not be. Cognition, 813:263–308, 1983.CrossRefGoogle Scholar
  2. S. Benferhat, D. Dubois, S. Kaci, and H. Prade. Bipolar possibility theory in preference modeling: Representation, fusion, and optimal solutions. Information Fusion, 7:135–150, 2006.Google Scholar
  3. A. J. Boyce. Mapping diversity: A comparative study of some numerical methods. In A. J. Cole, editor, Numerical Taxonomy, pages 1–31. Academic Press, London, 1969.Google Scholar
  4. L. Brooks. Nonanalytic concept formation and memory for instances. In E. Rosch and B. B. Lloyd, editors, Cognition and Categorization, pages 169–211. Lawrence Erlbaum, Hillsdale, NJ, 1978.Google Scholar
  5. A. J. Cain and G. A. Harrison. An analysis of the taxonomist’s judgement of affinity. Proc. Zool. Soc. Lond., 131:85–98, 1958.Google Scholar
  6. B. De Baets and H. De Meyer. Transitivity-preserving fuzzification schemes for cardinality-based similarity measures. European Journal of Operational Research, 160:726–740, 2003.Google Scholar
  7. B. De Baets and R. Mesiar. Metrics and t-equalities. Journal of Mathematical Analysis and Applications, 267:531–547, 2002.zbMATHCrossRefMathSciNetGoogle Scholar
  8. B. De Baets, H. De Meyer, and H. Naessens. A class of rational cardinality-based similarity measures. Journal of Computational and Applied Mathematics, 132:51–69, 2001.zbMATHCrossRefMathSciNetGoogle Scholar
  9. D. Dubois and H. Prade. A unifying view of comparison indices in a fuzzy set-theoretic framework. In Ronald R. Yager, editor, Fuzzy Set and Possibility Theory Recent Developments, pages 3–13. Pergamon Press, New York, NY, 1982.Google Scholar
  10. D. Dubois, H. Prade, and C. Testemale. Weighted fuzzy pattern matching. Fuzzy Sets and Systems, 28:313–331, 1988.zbMATHCrossRefMathSciNetGoogle Scholar
  11. R. French. The Subtlety of Sameness. MIT Press, 1995.Google Scholar
  12. P. Gambaryan. Taxonomic analysis of the genus pinus 1. Izvest. Akad. Nauk Armen. SRR, Biol. Nauki, 18(8):75–81, 1965.Google Scholar
  13. D. Gentner. Structure mapping: A theorical view for analogy. Cognitive Science, 7:155–170, 1983.CrossRefGoogle Scholar
  14. D. Gentner and J. Medina. Similarity and the development of rules. In S. A. Sloman and L. J. Rips, editors, Similarity and Symbols in Human Thinking, pages 177–211. MIT Press, Cambridge, Massachusetts, 1998.Google Scholar
  15. R. L. Goldstone, D. L. Medin, and D. Gentner. Relational similarity and the non-independence of features in similarity judgements. Cognitive Psychology, 23:222–262, 1991.CrossRefGoogle Scholar
  16. R. M. Gregson. Psychometrics of Similarity. Academic Press, New York, 1975.Google Scholar
  17. A. Hadj Ali, D. Dubois, and H. Prade. Implementing fuzzy reasoning with closeness and neglibility relations. In Proceedings of the 9th IFSA World Congress, pages 363–368, Vancouver, July 2001.Google Scholar
  18. D. Hofstader. Fluid Concepts and Creative Analogy. Harper Collins, 1995.Google Scholar
  19. K. J. Holyoak and P. Thagard. The analogical mind. American Psychologist, 51(1):35–44, 1997.CrossRefGoogle Scholar
  20. P. Jaccard. Nouvelles recherches sur la distribution florale. Bulletin de la Societe de Vaud des Sciences Naturelles, 44:223, 1908.Google Scholar
  21. C. L. Krumhansl. Concerning the applicability of geometric models to similarity data: The interrelationship between similarity and spatial density. Psychological Review, 85(5):445–463, 1978.CrossRefGoogle Scholar
  22. E. B. Lynch, J. D. Coley, and D. L. Medin. Tall is typical: Central tendency, ideal dimensions and graded category structure among tree experts. Memory and Cognition, 28:41–50, 2000.Google Scholar
  23. A. B. Markam and D. Gentner. Structural alignment during similarity comparisons. Cognitive Psychology, 25:431–467, 1993.CrossRefGoogle Scholar
  24. R. Nosofsky. Exemplars, prototypes, and similarity rules. In A. Healy, S. Kosslyn, and R. Shriffin, editors, From Learning Theory to Connectionist Theory: Essays in Honor of William K. Estes, pages 149–167. Lawrence Erlbaum, Hillsdale, NJ, 1992.Google Scholar
  25. S. Parsons. Qualitative probability and order of magnitude reasoning. International Journal of Uncertainty, Fuzziness, and Knowledge-Based Systems, 11(3):373–390, 2003.zbMATHCrossRefMathSciNetGoogle Scholar
  26. O. Raiman. Order of magnitude reasoning. Artificial Intelligence, 51(1): 11–38, 1991.CrossRefGoogle Scholar
  27. M. J. Ratterman and D. Gentner. Analogy and similarity: Determinants of accessibility and inferential soundness. In Proceedings of the 9th Annual Conference of the Cognitive Science Society, pages 23–25, 1987.Google Scholar
  28. L. Rips, E. Shoben, and E. Smith. Semantic distance and the verification of semantic relations. J. of Verbal Learning and Verbal Behaviour, 12:1–20, 1973.CrossRefGoogle Scholar
  29. R. Rosch and C. B. Mervis. Family resemblances: Studies in the internal structure of categories. Cognitive Psychology, 7:382–439, 1975.Google Scholar
  30. E. Rosch. Cognitive reference points. Cognitive Psychology, 7(5):532–547, 1975.CrossRefGoogle Scholar
  31. S. Santini and R. Jain. Similarity measures. IEEE Transactions on Pattern Analysis and Machine Intelligence, 21(9):871–883, 1999.CrossRefGoogle Scholar
  32. S. A. Sloman and L. J. Rips. Similarity and Symbols in Human Thinking. MIT Press, Cambridge, MA, 1998.Google Scholar
  33. P. H. A. Sneath. The application of numerical taxonomy to medical problems. In Mathematics and Computer Science in Biology and Medicine, pages 81–91. Her Majesty’s Stationery Office, London, 1965.Google Scholar
  34. R. R. Sokal and P. H. Sneath. Principles of Numerical Taxonomy. Freeman, San Francisco, CA, 1963.Google Scholar
  35. Y. Tolinas, S. Panas, and L. Tsoukalas. Generalized fuzzy indices for similarity matching. Fuzzy Sets and Systems, 120(2):255–270, 2001.CrossRefMathSciNetGoogle Scholar
  36. E. Trillas and L. Valverde. An inquiry into indistinguishability operators. In H. Skala, S. Termini, and E. Trillas, editors, Aspects of Vagueness, pages 231–256. Reidel, New York, 1984.Google Scholar
  37. A. Tversky. Features of similarity. Psychol. Rev., 84:327–352, 1977.CrossRefGoogle Scholar
  38. A. Tversky and I. Gaiti. Similarity, separability, and the triangle inequality. Psychological Review, 89(2):123–154, 1982.CrossRefGoogle Scholar
  39. L. A. Zadeh. Fuzzy sets as a basis for a theory of possibility. Fuzzy Sets and Systems, 1(1):3–28, 1978.zbMATHCrossRefMathSciNetGoogle Scholar

Copyright information

© CISM, Udine 2008

Authors and Affiliations

  • Thomas Sudkamp
    • 1
  1. 1.Department of Computer ScienceWright State UniversityDaytonUSA

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