Coarsening of fuzzy partitions

A vague partition U of a finite universal set X into c clusters, where each cluster is described by a fuzzy set on X, is considered. The concept of p-level sets [3] of fuzzy sets is extended to p-level matrices of fuzzy partitions. A method of gradual coarsening of U based on a sequence of p-level matrices derived from the membership grades of clusters of U is suggested. Modifications of p-level matrices to extended p-level matrices and to strict p-level matrices are proposed.

[1]  James M. Keller,et al.  A possibilistic fuzzy c-means clustering algorithm , 2005, IEEE Transactions on Fuzzy Systems.

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

[3]  Martin Kalina,et al.  Coarsening of fuzzy sets , 2013, 2013 IEEE 11th International Symposium on Intelligent Systems and Informatics (SISY).

[4]  T. Radecki.  LEVEL FUZZY SETS , 1977 .

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

[6]  Sankar K. Pal,et al.  Rough Set Based Generalized Fuzzy $C$ -Means Algorithm and Quantitative Indices , 2007, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[7]  Richard Weber,et al.  Soft clustering - Fuzzy and rough approaches and their extensions and derivatives , 2013, Int. J. Approx. Reason..

[8]  Etienne Kerre,et al.  The cutting of compositions , 1994 .

[9]  W. Peizhuang.  Pattern Recognition with Fuzzy Objective Function Algorithms (James C. Bezdek) , 1983 .

[10]  Witold Pedrycz,et al.  Rough–Fuzzy Collaborative Clustering , 2006, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[11]  Witold Pedrycz,et al.  Shadowed c-means: Integrating fuzzy and rough clustering , 2010, Pattern Recognit..

[12]  Slavka Bodjanova,et al.  Comparison of fuzzy partitions based on their α-cuts , 1999, Fuzzy Sets Syst..

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

[14]  D. Dubois,et al.  Fundamentals of fuzzy sets , 2000 .