A weighted fuzzy c

A fuzzy clustering model for fuzzy data is proposed. The model is based on a 'weighted' dissimilarity measure for comparing pairs of fuzzy data, composed by two distances, the so-called center (mode) distance and spread distance. The peculiarity of the proposed fuzzy clustering model is the objective estimation, incorporated in the clustering procedure, of suitable weights concerning the distance measures of the center and the spreads of the fuzzy data. In this way, the model objectively tunes the influence of the two components of the fuzzy data (center and spreads) for computing the mode and spread centroids in the fuzzy partitioning process. In order to show the performance of the proposed clustering algorithm, a simulation study and two illustrative applications are discussed.

[1]  Deng Yong,et al.  A new similarity measure of generalized fuzzy numbers and its application to pattern recognition , 2004 .

[2]  Miin-Shen Yang,et al.  Similarity measures of intuitionistic fuzzy sets based on Hausdorff distance , 2004, Pattern Recognit. Lett..

[3]  Miin-Shen Yang,et al.  Fuzzy clustering algorithms for mixed feature variables , 2004, Fuzzy Sets Syst..

[4]  E. Hisdal.  Conditional possibilities independence and noninteraction , 1978 .

[5]  James M. Keller,et al.  Analysis and efficient implementation of a linguistic fuzzy c-means , 2002, IEEE Trans. Fuzzy Syst..

[6]  Miin-Shen Yang,et al.  On a class of fuzzy c-numbers clustering procedures for fuzzy data , 1996, Fuzzy Sets Syst..

[7]  R. Goetschel,et al.  Topological properties of fuzzy numbers , 1983 .

[8]  Witold Pedrycz,et al.  A parametric model for fusing heterogeneous fuzzy data , 1996, IEEE Trans. Fuzzy Syst..

[9]  Edwin Diday,et al.  Symbolic clustering using a new dissimilarity measure , 1991, Pattern Recognit..

[10]  Renato Coppi,et al.  A theoretical framework for data mining: the informational paradigm , 2002 .

[11]  M. Sato,et al.  Fuzzy clustering model for fuzzy data , 1995, Proceedings of 1995 IEEE International Conference on Fuzzy Systems..

[12]  CoppiRenato.  A theoretical framework for data mining , 2002 .

[13]  W. Näther.  On random fuzzy variables of second order and their application to linear statistical inference with fuzzy data , 2000 .

[14]  Pierpaolo D'Urso,et al.  Three-way fuzzy clustering models for LR fuzzy time trajectories , 2003, Comput. Stat. Data Anal..

[15]  Sadaaki Miyamoto,et al.  Fuzzy clustering of data with uncertainties using minimum and maximum distances based on L/sub 1/ metric , 2001, Proceedings Joint 9th IFSA World Congress and 20th NAFIPS International Conference (Cat. No. 01TH8569).

[16]  Przemyslaw Grzegorzewski,et al.  Distances between intuitionistic fuzzy sets and/or interval-valued fuzzy sets based on the Hausdorff metric , 2004, Fuzzy Sets Syst..

[17]  James C. Bezdek,et al.  Pattern Recognition with Fuzzy Objective Function Algorithms , 1981, Advanced Applications in Pattern Recognition.

[18]  Abraham Kandel,et al.  On fuzzy correlations , 2001, IEEE Trans. Syst. Man Cybern. Part B.

[19]  Miin-Shen Yang,et al.  Fuzzy clustering on LR-type fuzzy numbers with an application in Taiwanese tea evaluation , 2005, Fuzzy Sets Syst..

[20]  Lotfi A. Zadeh,et al.  Fuzzy Sets , 1996, Inf. Control..

[21]  K. Chidananda Gowda,et al.  Symbolic clustering using a new similarity measure , 1992, IEEE Trans. Syst. Man Cybern..

[22]  J. MacQueen.  Some methods for classification and analysis of multivariate observations , 1967 .

[23]  Thierry Denoeux,et al.  Principal component analysis of fuzzy data using autoassociative neural networks , 2004, IEEE Transactions on Fuzzy Systems.

[24]  Hans-Jürgen Zimmermann,et al.  Fuzzy Set Theory - and Its Applications , 1985 .

[25]  C. Pappis,et al.  A comparative assessment of measures of similarity of fuzzy values , 1993 .

[26]  Ferenc Szeifert,et al.  Data-driven generation of compact, accurate, and linguistically sound fuzzy classifiers based on a decision-tree initialization , 2003, Int. J. Approx. Reason..

[27]  Isabelle Bloch,et al.  On fuzzy distances and their use in image processing under imprecision , 1999, Pattern Recognit..

[28]  P. Groenen,et al.  Data analysis, classification, and related methods , 2000 .

[29]  Pierpaolo D'Urso,et al.  A possibilistic approach to latent component analysis for symmetric fuzzy data , 2005, Fuzzy Sets Syst..

[30]  Miin-Shen Yang,et al.  Fuzzy clustering procedures for conical fuzzy vector data , 1999, Fuzzy Sets Syst..

[31]  Janusz Kacprzyk,et al.  Distances between intuitionistic fuzzy sets , 2000, Fuzzy Sets Syst..

[32]  Pierpaolo D'Urso,et al.  Fuzzy Time Arrays and Dissimilarity Measures For Fuzzy Time Trajectories , 2000 .

[33]  Azriel Rosenfeld,et al.  Fuzzy Digital Topology , 1979, Inf. Control..

[34]  Rami Zwick,et al.  Measures of similarity among fuzzy concepts: A comparative analysis , 1987, Int. J. Approx. Reason..

[35]  Paolo Giordani,et al.  Principal Component Analysis of symmetric fuzzy data , 2004, Comput. Stat. Data Anal..

[36]  Witold Pedrycz,et al.  Two nonparametric models for fusing heterogeneous fuzzy data , 1998, IEEE Trans. Fuzzy Syst..

[37]  Pierpaolo D'Urso,et al.  Fuzzy K-means clustering models for triangular fuzzy time trajectories , 2002 .

[38]  Yun Kyong Kim,et al.  Some properties of a new metric on the space of fuzzy numbers , 2004, Fuzzy Sets Syst..