One Solution for Proving Convergence of Picture Fuzzy Clustering Method

Fuzzy clustering on the picture fuzzy set is widely applied to practical problems. However, the assessment on its convergence has not been considered yet. In this paper, we investigate the theoretical analysis of FC-PFS especially the convergence of the algorithm. Future directions are also discussed.

[1]  Le Hoang Son,et al.  A New Approach to Multi-variable Fuzzy Forecasting Using Picture Fuzzy Clustering and Picture Fuzzy Rule Interpolation Method , 2014, KSE.

[2]  Hui Xiong,et al.  A Generalization of Distance Functions for Fuzzy $c$ -Means Clustering With Centroids of Arithmetic Means , 2012, IEEE Transactions on Fuzzy Systems.

[3]  Le Hoang Son,et al.  Picture fuzzy clustering for complex data , 2016, Eng. Appl. Artif. Intell..

[4]  Hamido Fujita,et al.  Interpolative picture fuzzy rules: A novel forecast method for weather nowcasting , 2016, 2016 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE).

[5]  Pierpaolo D'Urso,et al.  Informational Paradigm, management of uncertainty and theoretical formalisms in the clustering framework: A review , 2017, Inf. Sci..

[6]  Lawrence O. Hall,et al.  Convergence of the Single-Pass and Online Fuzzy C-Means Algorithms , 2011, IEEE Transactions on Fuzzy Systems.

[7]  Bui Cong Cuong,et al.  Picture fuzzy sets , 2015 .

[8]  Le Hoang Son,et al.  A novel automatic picture fuzzy clustering method based on particle swarm optimization and picture composite cardinality , 2016, Knowl. Based Syst..

[9]  Soheil Sadi-Nezhad,et al.  A new fuzzy clustering algorithm based on multi-objective mathematical programming , 2014, TOP.

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

[11]  Le Hoang Son,et al.  Some novel hybrid forecast methods based on picture fuzzy clustering for weather nowcasting from satellite image sequences , 2016, Applied Intelligence.