Fuzzy Prototypes: From a Cognitive View to a Machine Learning Principle

Cognitive psychology works have shown that the cognitive representation of categories is based on a typicality notion: all objects of a category do not have the same representativeness, some are more characteristic or more typical than others, and better exemplify their category. Categories are then defined in terms of prototypes, i.e. in terms of their most typical elements. Furthermore, these works showed that an object is all the more typical of its category as it shares many features with the other members of the category and few features with the members of other categories.

[1]  Janusz Kacprzyk,et al.  LINGUISTIC SUMMARIES OF DATA USING FUZZY LOGIC , 2001 .

[2]  E. Rosch,et al.  Family resemblances: Studies in the internal structure of categories , 1975, Cognitive Psychology.

[3]  Didier Dubois,et al.  Fuzzy sets and systems ' . Theory and applications , 2007 .

[4]  Rajesh N. Davé,et al.  Characterization and detection of noise in clustering , 1991, Pattern Recognit. Lett..

[5]  James M. Keller,et al.  A possibilistic approach to clustering , 1993, IEEE Trans. Fuzzy Syst..

[6]  James C. Bezdek,et al.  Fuzzy mathematics in pattern classification , 1973 .

[7]  Rudolf Kruse,et al.  Data Summarisation by Typicality-based Clustering for Vectorial and Non Vectorial Data , 2006, 2006 IEEE International Conference on Fuzzy Systems.

[8]  Janusz Kacprzyk,et al.  A Fuzzy Logic Based Approach to Linguistic Summaries of Databases , 2000 .

[9]  Bernadette Bouchon-Meunier,et al.  Discrimination power of measures of comparison , 2000, Fuzzy Sets Syst..

[10]  Anil K. Jain,et al.  Data clustering: a review , 1999, CSUR.

[11]  Marcin Detyniecki,et al.  Mathematical Aggregation Operators and their Application to Video Querying , 2000 .

[12]  Ronald R. Yager,et al.  On the Application of a class of MICA operators , 1995, Int. J. Uncertain. Fuzziness Knowl. Based Syst..

[13]  Ronald R. Yager A Human Directed Approach for Data Summarization , 2006, 2006 IEEE International Conference on Fuzzy Systems.

[14]  Bernadette Bouchon-Meunier,et al.  Fuzzy Prototypes Based on Typicality Degrees , 2004, Fuzzy Days.

[15]  Marie-Jeanne Lesot TYPICALITY-BASED CLUSTERING , 2006 .

[16]  M. Posner,et al.  On the genesis of abstract ideas. , 1968, Journal of experimental psychology.

[17]  Marie-Jeanne Lesot Gustafson-Kessel-like clustering algorithm based on typicality degrees , 2006 .

[18]  W. Silvert Symmetric Summation: A Class of Operations on Fuzzy Sets , 1979 .

[19]  D. Kibler,et al.  Instance-based learning algorithms , 2004, Machine Learning.

[20]  M. Mizumoto Pictorial representations of fuzzy connectives, Part II: cases of compensatory operators and self-dual operators , 1989 .

[21]  S. Muller,et al.  A fuzzy logic based approach for semiological analysis of microcalcifications in mammographic images , 1997 .

[22]  R. Mesiar,et al.  Aggregation operators: properties, classes and construction methods , 2002 .

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

[24]  F. Klawonn,et al.  Fuzzy Cluster Analysis: Methods for Classification, Data Analysis and Image Recognition , 1999 .

[25]  Maria Rifqi Constructing prototypes from large databases , 1996 .

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

[27]  J. C. Dunn,et al.  A Fuzzy Relative of the ISODATA Process and Its Use in Detecting Compact Well-Separated Clusters , 1973 .

[28]  Eleanor Rosch,et al.  Principles of Categorization , 1978 .

[29]  James C. Bezdek,et al.  A mixed c-means clustering model , 1997, Proceedings of 6th International Fuzzy Systems Conference.

[30]  L. A. Zadeh,et al.  A note on prototype theory and fuzzy sets , 1982, Cognition.

[31]  Donald Gustafson,et al.  Fuzzy clustering with a fuzzy covariance matrix , 1978, 1978 IEEE Conference on Decision and Control including the 17th Symposium on Adaptive Processes.

[32]  Maria Rifqi,et al.  Fuzzy Techniques in Mammographic Image Processing , 2000 .

[33]  Marie-Jeanne Lesot Similarity , typicality and fuzzy prototypes for numerical data , 2005 .

[34]  Heiko Timm,et al.  A modification to improve possibilistic fuzzy cluster analysis , 2002, 2002 IEEE World Congress on Computational Intelligence. 2002 IEEE International Conference on Fuzzy Systems. FUZZ-IEEE'02. Proceedings (Cat. No.02CH37291).

[35]  Abraham Kandel,et al.  On the Theory of Typicality , 1995, Int. J. Uncertain. Fuzziness Knowl. Based Syst..

[36]  M. Mizumoto Pictorial representations of fuzzy connectives, part I: cases of t-norms, t-conorms and averaging operators , 1989 .