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.
Keywords
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Armstrong, S.L., Gleitman, L.R., Gleitman, H.: What some concepts might not be. Cognition 13(3), 263–308 (1983)
Batagelj, V., Bren, M.: Comparing resemblance measures. Journal of Classification 12, 73–90 (1995)
Baulieu, F.B.: A classification of presence/absence based dissimilarity coefficients. Journal of Classification 6, 233–246 (1989)
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)
Bouchon-Meunier, B., Rifqi, M., Bothorel, S.: Towards general measures of comparison of objects. Fuzzy Sets and Systems 84(2), 143–153 (1996)
Bush, R.R., Mosteller, F.: A model for stimulus generalization and discrimination. Psychological Review 58, 413–423 (1951)
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)
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)
Cohen, B., Murphy, G.L.: Models of concepts. Cognitive Science 8, 27–58 (1984)
Eisler, H., Ekman, G.: A mechanism of subjective similarity. Acta Psychologica 16, 1–10 (1959)
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)
Fagin, R., Kumar, R., Sivakumar, D.: Comparing top k lists. SIAM Journal on Discrete Mathematics 17(1), 134–160 (2003)
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)
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)
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)
Fuhrmann, G.: Note on the integration of prototype theory and fuzzy-set theory. Synthese 86, 1–27 (1991)
Gregson, R.: Psychometrics of similarity. Academic Press, New York (1975)
Hampton, J.A.: A demonstration of intransitivity in natural categories. Cognition 12(2), 151–164 (1982)
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)
Kamp, H., Partee, B.: Prototype theory and compositionality. Cognition 57(2), 129–191 (1995)
Kleiber, G.: Prototype et prototypes. In: Sémantique et Cognition. Editions du C.N.R.S, Paris (1991)
Lerman, I.C.: Indice de similarité et préordonnance associée. In: Séminaire Sur Les Ordres Totaux Finis, pp. 233–243. Aix-en-Provence (1967)
Lesot, M.J.: Similarity, typicality and fuzzy prototypes for numerical data. Res-Systemica 5 (2005)
Lesot, M.J.: Typicality-based clustering. International Journal of Information Technology and Intelligent Computing 1(2), 279–292 (2006)
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)
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)
Lesot, M.J., Mouillet, L., Bouchon-Meunier, B.: Fuzzy prototypes based on typicality degrees. In: Fuzzy Days 2004, pp. 125–138. Springer, Dortmund (2004)
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)
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)
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)
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)
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)
Osherson, D.N., Smith, E.E.: On the adequacy of prototype theory as a theory of concepts. Cognition 9, 35–58 (1981)
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)
Pappis, C.P., Karacapilidis, N.: A comparative assessment of measures of similarity of fuzzy values. Fuzzy Sets and Systems 56, 171–174 (1993)
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)
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)
Rifqi, M., Berger, V., Bouchon-Meunier, B.: Discrimination power of measures of comparison. Fuzzy Sets and Systems 110, 189–196 (2000)
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)
Rifqi, M., Detyniecki, M., Bouchon-Meunier, B.: Discrimination power of measures of resemblance. In: IFSA 2003, Istanbul (2003)
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)
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)
Rosch, E.: Principles of categorization. In: Rosch, E., Lloyd, B.B. (eds.) Cognition and Categorization, pp. 27–48. Laurence Erlbaum Associates, Hillsdale (1978)
Santini, S., Jain, R.: Similarity measures. IEEE Transactions on Pattern Analysis and Machine Intelligence 21(9) (1999)
Shiina, K.: A fuzzy-set-theoretic feature model and its application to asymmetric data analysis. Japanese Psychological Research 30(3), 95–104 (1988)
Torgerson, W.S.: Multidimensional scaling of similarity. Psychometrika 30, 379–393 (1965)
Tversky, A.: Features of similarity. Psychological Review 84, 327–352 (1977)
Tversky, A., Kahneman, D.: Extensional versus intuitive reasoning: The conjunction fallacy in probability judgment. Psychological Review 90(4), 293–315 (1983)
Wittgenstein, L.: Philosophical investigations. Macmillan, NewYork (1953)
Zadeh, L.A.: A note on prototype theory and fuzzy sets. Cognition 12, 291–297 (1982)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights 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)