Abstract
Credibilistic clustering is a new clustering method using the credibility measure in fuzzy clustering. Zhou et al. (2014) presented the clustering model of credibilistic clustering together with a credibilistic clustering algorithm for solving the optimization model. In this paper, a further investigation on credibilistic clustering is made. Within the solution architecture of alternating cluster estimation, a family of general credibilistic clustering algorithms are designed for solving the credibilistic clustering model. Moreover, a new credibilistic clustering algorithm is recommended for the real applications. Numerical examples based on randomly generated data sets and real data sets are presented to illustrate the performance and effectiveness of the credibilistic clustering algorithms from different aspects. Results comparing with the fuzzy \(c\)-means algorithm and the possibilistic clustering algorithms show that the proposed credibilistic clustering algorithms can survive from the coincident problem and the noisy environments, and provide the clustering results with high overall accuracy.



Similar content being viewed by others
References
Bezdek, J. C. (1981). Pattern recognition with fuzzy objective function algorithms. New York: Plenum Press.
Box, G. E. P., & Jenkins, G. M. (1970). Time series analysis, forecasting and control. San Francisco: Holden-Day.
Cardoso, M. G. M. S., & Moutinho, L. (2003). Measurement and analysis for marketing. Journal of Targeting, 12(1), 27–41.
Charytanowicz, M., Niewczas, J., Kulczycki, P., Kowalski, P. A., Lukasik, S., & Zak, S. (2010). Complete gradient clustering algorithm for features analysis of X-ray images. In E. Pietka & J. Kawa (Eds.), Information technologies in biomedicine (pp. 15–24). Berlin, Heidelberg: Springer.
Chen, X., & Ralescu, D. A. (2012). B-spline method of uncertain statistics with applications to estimate travel distance. Journal of Uncertain Systems, 6(4), 256–262.
Cordon, O., Herrera, F., & Sanchez, L. (1999). Solving electrical distribution problems using hybrid evolutionary data analysis techniques. Applied Intelligence, 10(1), 5–24.
Fisher, R. A. (1936). The use of multiple measurements in taxonomic problems. Annals of Eugenics, 7(2), 179–188.
Forina, M., Leardi, R., Armanino, C., & Lanteri, S. (1988). An extendable package of programs for data exploration, classification and correlation. Amsterdam: Elsevier.
Kahraman, H. T., Sagiroglu, S., & Colak, I. (2013). The development of intuitive knowledge classifier and the modeling of domain dependent data. Knowledge-Based Systems, 37, 283–295.
Krishnapuram, R., & Keller, J. M. (1993). A possibilistic approach to clustering. IEEE Transactions on Fuzzy Systems, 1(2), 98–110.
Krishnapuram, R., & Keller, J. M. (1996). The possibilistic \(c\)-means algorithm: Insights and recommendations. IEEE Transactions on Fuzzy Systems, 4(3), 385–393.
Li, X., & Liu, B. (2006). A sufficient and necessary condition for credibility measures. International Journal of Uncertainty, Fuzziness and Knowledge-based Systems, 14(5), 527–535.
Li, X., & Lo, H. K. (2014). An energy-efficient scheduling and speed control approach for metro rail operations. Transportation Research Part B, 64, 73–89.
Li, X., Qin, Z., & Kar, S. (2010). Mean-variance-skewness model for portfolio selection with fuzzy returns. European Journal of Operational Research, 202(1), 239–247.
Li, X., Wong, H. S., & Wu, S. (2012). A fuzzy minimax clustering model and its applications. Information Sciences, 186(1), 114–125.
Liu, B. (2002a). Toward fuzzy optimization without mathematical ambiguity. Fuzzy Optimization and Decision Making, 1(1), 43–63.
Liu, B. (2002b). Theory and practice of uncertain programming. Heidelberg: Physica-Verlag.
Liu, B. (2004). Uncertainty theory: An introduction to its axiomatic foundations. Berlin: Springer.
Liu, B. (2006). A survey of credibility theory. Fuzzy Optimization and Decision Making, 5(4), 387–408.
Liu, B., & Liu, Y. (2002). Expected value of fuzzy variable and fuzzy expected value models. IEEE Transactions on Fuzzy Systems, 10(4), 445–450.
Liu, W. Y., & Jiang, J. L. (2014). A new Chinese character recognition approach based on the fuzzy clustering analysis. Neural Computing & Applications, 25(2), 421–428.
Mackey, M. C., & Glass, L. (1977). Oscillation and chaos in physiological control systems. Science, 197(4300), 287–289.
Nahmias, S. (1978). Fuzzy variables. Fuzzy Sets and Systems, 1(2), 97–110.
Ni, Y., & Zhao, Z. (2014). Two-agent scheduling problem under fuzzy environment. Journal of Intelligent Manufacturing. doi:10.1007/s10845-014-0992-6
Quah, C. H. (2014). Revisiting business cycles in the Eurozone: A fuzzy clustering and discriminant approach. Acta Oeconomica, 64(2), 161–180.
Runkler, T. A., & Bezdek, J. C. (1999). Alternating cluster estimation: A new tool for clustering and function approximation. IEEE Transactions on Fuzzy Systems, 7(4), 377–393.
Singh, A. K., & Purohit, N. (2014). An optimised fuzzy clustering for wireless sensor networks. International Journal of Electronics, 101(8), 1027–1041.
Tjhi, W. C., & Chen, L. (2007). Possibilistic fuzzy co-clustering of large document collections. Pattern Recognition, 40(12), 3452–3466.
Wang, C. H., & Kuo, W. (2007). Identification of control chart patterns using wavelet filtering and robust fuzzy clustering. Journal of Intelligent Manufacturing, 18(3), 343–350.
Wang, Q., Zhou, J., & Hung, C. C. (2014). A general framework for constructing possibilistic membership functions in alternating cluster estimation. International Journal of Innovative Computing, Information and Control, 10(6), 2035–2049.
Wen, P., Zhou, J., & Zheng, L. (2008). Hybrid methods of spatial credibilistic clustering and particle swarm optimization in high noise image segmentation. International Journal of Fuzzy Systems, 10(3), 174–184.
Wen, P., Zhou, J., & Zheng, L. (2011). A modified hybrid method of spatial credibilistic clustering and particle swarm optimization. Soft Computing, 15(5), 855–865.
Yang, M. S., & Wu, K. L. (2006). Unsupervised possibilistic clustering. Pattern Recognition, 39(1), 5–21.
Yang, X., & Gao, J. (2013). Uncertain differential games with application to capitalism. Journal of Uncertainty Analysis and Applications, 1(1), 17.
Yao, K., & Li, X. (2012). Uncertain alternating renewal process and its application. IEEE Transactions on Fuzzy Systems, 20(6), 1154–1160.
Zadeh, L. A. (1978). Fuzzy sets as a basis for a theory of possibility. Fuzzy Sets and Systems, 1(1), 3–28.
Zadeh, L. A. (1979). A theory of approximate reasoning. In J. Hayes, D. Michie, & R. M. Thrall (Eds.), Mathematical Frontiers of the Social and Policy Sciences (pp. 69–129). Boulder, CO: Westview Press.
Zhou, J., Cao, L., & Yang, N. (2013). On the convergence of some possibilistic clustering algorithms. Fuzzy Optimization and Decision Making, 12(4), 415–432.
Zhou, J., & Hung, C. C. (2007). A generalized approach to possibilistic clustering algorithms. International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, 15(Suppl 2), 117–138.
Zhou, J., Wang, Q., Hung, C. C., & Yang, F. (2014). Credibilistic clustering: The model and algorithms. Technical report.
Acknowledgments
This work was supported by grants from the Innovation Program of Shanghai Municipal Education Commission (No. 13ZS065), the Shanghai Philosophy and Social Science Planning Project (No. 2012BGL006), and the National Social Science Foundation of China (No. 13CGL057).
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Zhou, J., Wang, Q., Hung, CC. et al. Credibilistic clustering algorithms via alternating cluster estimation. J Intell Manuf 28, 727–738 (2017). https://doi.org/10.1007/s10845-014-1004-6
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10845-014-1004-6