Skip to main content

Cognition-Inspired Fuzzy Modelling

  • Chapter
Advances in Computational Intelligence (WCCI 2012)

Part of the book series: Lecture Notes in Computer Science ((LNISA,volume 7311))

Included in the following conference series:

Abstract

This chapter presents different notions used for fuzzy modelling that formalize fundamental concepts used in cognitive psychology. From a cognitive point of view, the tasks of categorization, pattern recognition or generalization lie in the notions of similarity, resemblance or prototypes. The same tasks are crucial in Artificial Intelligence to reproduce human behaviors. As most real world concepts are messy and open-textured, fuzzy logic and fuzzy set theory can be the relevant framework to model all these key notions.

On the basis of the essential works of Rosch and Tversky, and on the critics formulated on the inadequacy of fuzzy logic to model cognitive concepts, we study a formal and computational approach of the notions of similarity, typicality and prototype, using fuzzy set theory. We propose a framework to understand the different properties and possible behaviors of various families of similarities. We highlight their semantic specifics and we propose numerical tools to quantify these differences, considering different views. We propose also an algorithm for the construction of fuzzy prototypes that can be extended to a classification method.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Armstrong, S.L., Gleitman, L.R., Gleitman, H.: What some concepts might not be. Cognition 13(3), 263–308 (1983)

    Article  Google Scholar 

  2. Batagelj, V., Bren, M.: Comparing resemblance measures. Journal of Classification 12, 73–90 (1995)

    Article  MathSciNet  MATH  Google Scholar 

  3. Baulieu, F.B.: A classification of presence/absence based dissimilarity coefficients. Journal of Classification 6, 233–246 (1989)

    Article  MathSciNet  MATH  Google Scholar 

  4. Bouchon-Meunier, B., Coletti, G., Lesot, M.-J., Rifqi, M.: Towards a Conscious Choice of a Fuzzy Similarity Measure: A Qualitative Point of View. In: Hüllermeier, E., Kruse, R., Hoffmann, F. (eds.) IPMU 2010. LNCS, vol. 6178, pp. 1–10. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

  5. Bouchon-Meunier, B., Rifqi, M., Bothorel, S.: Towards general measures of comparison of objects. Fuzzy Sets and Systems 84(2), 143–153 (1996)

    Article  MathSciNet  MATH  Google Scholar 

  6. Bush, R.R., Mosteller, F.: A model for stimulus generalization and discrimination. Psychological Review 58, 413–423 (1951)

    Article  Google Scholar 

  7. Bělohlávek, R., Klir, G.J., Lewis, H.W., Way, E.C.: On the capability of fuzzy set theory to represent concepts. International Journal of General Systems 31(6), 569–585 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  8. Bělohlávek, R., Klir, G.J., Lewis, H.W., Way, E.C.: Concepts and fuzzy sets: Misunderstandings, misconceptions, and oversights. International Journal of Approximate Reasoning 51(1), 23–34 (2009)

    Article  Google Scholar 

  9. Cohen, B., Murphy, G.L.: Models of concepts. Cognitive Science 8, 27–58 (1984)

    Article  Google Scholar 

  10. Eisler, H., Ekman, G.: A mechanism of subjective similarity. Acta Psychologica 16, 1–10 (1959)

    Article  Google Scholar 

  11. Fagin, R., Kumar, R., Mahdian, M., Sivakumar, D., Vee, E.: Comparing and aggregating rankings with ties. In: Symposium on Principles of Database Systems, pp. 47–58 (2004)

    Google Scholar 

  12. Fagin, R., Kumar, R., Sivakumar, D.: Comparing top k lists. SIAM Journal on Discrete Mathematics 17(1), 134–160 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  13. Forest, J., Rifqi, M., Bouchon-Meunier, B.: Class segmentation to improve fuzzy prototype construction: Visualization and characterization of non homogeneous classes. In: IEEE World Congress on Computational Intelligence (WCCI 2006), Vancouver, pp. 555–559 (2006)

    Google Scholar 

  14. Forest, J., Rifqi, M., Bouchon-Meunier, B.: Segmentation de classes pour l’amélioration de la construction de prototypes flous: visualisation et caractérisation de classes non homogénes. In: Rencontres francophones sur la Logique Floue et ses Applications (LFA 2006), Toulouse, pp. 29–36 (2006)

    Google Scholar 

  15. Friedman, M., Ming, M., Kandel, A.: On the theory of typicality. International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 3(2), 127–142 (1995)

    Article  MathSciNet  MATH  Google Scholar 

  16. Fuhrmann, G.: Note on the integration of prototype theory and fuzzy-set theory. Synthese 86, 1–27 (1991)

    Article  MathSciNet  MATH  Google Scholar 

  17. Gregson, R.: Psychometrics of similarity. Academic Press, New York (1975)

    Google Scholar 

  18. Hampton, J.A.: A demonstration of intransitivity in natural categories. Cognition 12(2), 151–164 (1982)

    Article  Google Scholar 

  19. Hampton, J.A.: The role of similarity in natural categorization. In: Hahn, U., Ramscar, M. (eds.) Similarity and Categorization, pp. 13–28. Oxford University Press (2001)

    Google Scholar 

  20. Kamp, H., Partee, B.: Prototype theory and compositionality. Cognition 57(2), 129–191 (1995)

    Article  Google Scholar 

  21. Kleiber, G.: Prototype et prototypes. In: Sémantique et Cognition. Editions du C.N.R.S, Paris (1991)

    Google Scholar 

  22. Lerman, I.C.: Indice de similarité et préordonnance associée. In: Séminaire Sur Les Ordres Totaux Finis, pp. 233–243. Aix-en-Provence (1967)

    Google Scholar 

  23. Lesot, M.J.: Similarity, typicality and fuzzy prototypes for numerical data. Res-Systemica 5 (2005)

    Google Scholar 

  24. Lesot, M.J.: Typicality-based clustering. International Journal of Information Technology and Intelligent Computing 1(2), 279–292 (2006)

    Google Scholar 

  25. Lesot, M.J., Kruse, R.: Data summarisation by typicality-based clustering for vectorial data and nonvectorial data. In: IEEE International Conference on Fuzzy Systems (Fuzz-IEEE 2006), Vancouver, pp. 3011–3018 (2006)

    Google Scholar 

  26. Lesot, M.J., Kruse, R.: Gustafson-Kessel-like clustering algorithm based on typicality degrees. In: International Conference on Information Processing and Management of Uncertainty in Knowledge-Based Systems, IPMU 2006, Paris, pp. 1300–1307 (2006)

    Google Scholar 

  27. Lesot, M.J., Mouillet, L., Bouchon-Meunier, B.: Fuzzy prototypes based on typicality degrees. In: Fuzzy Days 2004, pp. 125–138. Springer, Dortmund (2004)

    Google Scholar 

  28. Lesot, M.-J., Rifqi, M.: Order-Based Equivalence Degrees for Similarity and Distance Measures. In: Hüllermeier, E., Kruse, R., Hoffmann, F. (eds.) IPMU 2010. LNCS, vol. 6178, pp. 19–28. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

  29. Lesot, M.J., Rifqi, M., Bouchon-Meunier, B.: Fuzzy prototypes: From a cognitive view to a machine learning principle. In: Bustince, H., Herrera, F., Montero, J. (eds.) Fuzzy Sets and Their Extensions: Representation, Aggregation and Models, pp. 431–452. Springer (2007)

    Google Scholar 

  30. Marsala, C., Bouchon-Meunier, B.: An adaptable system to construct fuzzy decision trees. In: North American Fuzzy Information Processing Society Annual Conference, NAFIPS 1999, New York, pp. 223–227 (1999)

    Google Scholar 

  31. Marsala, C., Rifqi, M.: Characterizing forest of fuzzy decision trees errors. In: 4th International Conference of the ERCIM Working Group on Compting & Statistics (ERCIM 2011), London (2011)

    Google Scholar 

  32. Omhover, J.-F., Rifqi, M., Detyniecki, M.: Ranking Invariance Based on Similarity Measures in Document Retrieval. In: Detyniecki, M., Jose, J.M., Nürnberger, A., van Rijsbergen, C.J.‘. (eds.) AMR 2005. LNCS, vol. 3877, pp. 55–64. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  33. Osherson, D.N., Smith, E.E.: On the adequacy of prototype theory as a theory of concepts. Cognition 9, 35–58 (1981)

    Article  Google Scholar 

  34. Pal, N., Pal, K., Bezdek, J.: A mixed c-means clustering model. In: IEEE International Conference on Fuzzy Systems, Fuzz-IEEE 1997, Barcelona, pp. 11–21 (1997)

    Google Scholar 

  35. Pappis, C.P., Karacapilidis, N.: A comparative assessment of measures of similarity of fuzzy values. Fuzzy Sets and Systems 56, 171–174 (1993)

    Article  MathSciNet  MATH  Google Scholar 

  36. Rick, A., Bothorel, S., Bouchon-Meunier, B., Muller, S., Rifqi, M.: Fuzzy techniques in mammographic image processing. In: Kerre, E., Nachtegael, M. (eds.) Fuzzy Techniques in Image Processing. STUDFUZZ, pp. 308–336. Springer (2000)

    Google Scholar 

  37. Rifqi, M.: Constructing prototypes from large databases. In: International Conference on Information Processing and Management of Uncertainty in Knowledge-Based Systems, IPMU 1996, Granada, pp. 301–306 (1996)

    Google Scholar 

  38. Rifqi, M., Berger, V., Bouchon-Meunier, B.: Discrimination power of measures of comparison. Fuzzy Sets and Systems 110, 189–196 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  39. Rifqi, M., Bothorel, S., Bouchon-Meunier, B., Muller, S.: Similarity and prototype based approach for classification of microcalcifications. In: IFSA 1997, Prague, pp. 123–128 (1997)

    Google Scholar 

  40. Rifqi, M., Detyniecki, M., Bouchon-Meunier, B.: Discrimination power of measures of resemblance. In: IFSA 2003, Istanbul (2003)

    Google Scholar 

  41. Rifqi, M., Lesot, M.J., Detyniecki, M.: Fuzzy order-equivalence for similarity measures. In: 27th North American Fuzzy Information Processing Society Annual Conference (NAFIPS 2008), New York (2008)

    Google Scholar 

  42. Rosch, E.: Cognitive development and the acquisition of language. In: On the Internal Structure of Perceptual and Semantic Categories, pp. 111–141. Academic Press, Oxford (1973)

    Google Scholar 

  43. Rosch, E.: Principles of categorization. In: Rosch, E., Lloyd, B.B. (eds.) Cognition and Categorization, pp. 27–48. Laurence Erlbaum Associates, Hillsdale (1978)

    Google Scholar 

  44. Santini, S., Jain, R.: Similarity measures. IEEE Transactions on Pattern Analysis and Machine Intelligence 21(9) (1999)

    Google Scholar 

  45. Shiina, K.: A fuzzy-set-theoretic feature model and its application to asymmetric data analysis. Japanese Psychological Research 30(3), 95–104 (1988)

    Google Scholar 

  46. Torgerson, W.S.: Multidimensional scaling of similarity. Psychometrika 30, 379–393 (1965)

    Article  Google Scholar 

  47. Tversky, A.: Features of similarity. Psychological Review 84, 327–352 (1977)

    Article  Google Scholar 

  48. Tversky, A., Kahneman, D.: Extensional versus intuitive reasoning: The conjunction fallacy in probability judgment. Psychological Review 90(4), 293–315 (1983)

    Article  Google Scholar 

  49. Wittgenstein, L.: Philosophical investigations. Macmillan, NewYork (1953)

    MATH  Google Scholar 

  50. Zadeh, L.A.: A note on prototype theory and fuzzy sets. Cognition 12, 291–297 (1982)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2012 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Rifqi, M. (2012). Cognition-Inspired Fuzzy Modelling. In: Liu, J., Alippi, C., Bouchon-Meunier, B., Greenwood, G.W., Abbass, H.A. (eds) Advances in Computational Intelligence. WCCI 2012. Lecture Notes in Computer Science, vol 7311. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-30687-7_9

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-30687-7_9

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-30686-0

  • Online ISBN: 978-3-642-30687-7

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics