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Fuzzy and possibilistic clustering for fuzzy data

Author

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  • Coppi, Renato
  • D’Urso, Pierpaolo
  • Giordani, Paolo

Abstract

The Fuzzy k-Means clustering model (FkM) is a powerful tool for classifying objects into a set of k homogeneous clusters by means of the membership degrees of an object in a cluster. In FkM, for each object, the sum of the membership degrees in the clusters must be equal to one. Such a constraint may cause meaningless results, especially when noise is present. To avoid this drawback, it is possible to relax the constraint, leading to the so-called Possibilistic k-Means clustering model (PkM). In particular, attention is paid to the case in which the empirical information is affected by imprecision or vagueness. This is handled by means of LR fuzzy numbers. An FkM model for LR fuzzy data is firstly developed and a PkM model for the same type of data is then proposed. The results of a simulation experiment and of two applications to real world fuzzy data confirm the validity of both models, while providing indications as to some advantages connected with the use of the possibilistic approach.

Suggested Citation

  • Coppi, Renato & D’Urso, Pierpaolo & Giordani, Paolo, 2012. "Fuzzy and possibilistic clustering for fuzzy data," Computational Statistics & Data Analysis, Elsevier, vol. 56(4), pages 915-927.
    • Handle: RePEc:eee:csdana:v:56:y:2012:i:4:p:915-927
    DOI: 10.1016/j.csda.2010.09.013
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    References listed on IDEAS

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    1. Renato Coppi & Paolo Giordani & Pierpaolo D’Urso, 2006. "Component Models for Fuzzy Data," Psychometrika, Springer;The Psychometric Society, vol. 71(4), pages 733-761, December.
    2. D'Urso, Pierpaolo & Giordani, Paolo, 2006. "A weighted fuzzy c-means clustering model for fuzzy data," Computational Statistics & Data Analysis, Elsevier, vol. 50(6), pages 1496-1523, March.
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    Cited by:

    1. Han, Yongming & Geng, Zhiqiang & Zhu, Qunxiong & Qu, Yixin, 2015. "Energy efficiency analysis method based on fuzzy DEA cross-model for ethylene production systems in chemical industry," Energy, Elsevier, vol. 83(C), pages 685-695.
    2. D'Urso, Pierpaolo & Disegna, Marta & Massari, Riccardo & Osti, Linda, 2016. "Fuzzy segmentation of postmodern tourists," Tourism Management, Elsevier, vol. 55(C), pages 297-308.
    3. Soheil Sadi-Nezhad & Kaveh Khalili-Damghani & Ameneh Norouzi, 2015. "A new fuzzy clustering algorithm based on multi-objective mathematical programming," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 23(1), pages 168-197, April.
    4. Pierpaolo D’Urso & Livia Giovanni & Riccardo Massari, 2015. "Trimmed fuzzy clustering for interval-valued data," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 9(1), pages 21-40, March.
    5. Pierpaolo D’Urso & María Ángeles Gil, 2017. "Fuzzy data analysis and classification," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 11(4), pages 645-657, December.
    6. Pierpaolo D'Urso & Marta Disegna & Riccardo Massari & Linda Osti, 2014. "Fuzzy segmentation in postmodern consumers," BEMPS - Bozen Economics & Management Paper Series BEMPS20, Faculty of Economics and Management at the Free University of Bozen.
    7. Fernando Reche & María Morales & Antonio Salmerón, 2020. "Statistical Parameters Based on Fuzzy Measures," Mathematics, MDPI, vol. 8(11), pages 1-20, November.
    8. Coletti, Giulianella & Gervasi, Osvaldo & Tasso, Sergio & Vantaggi, Barbara, 2012. "Generalized Bayesian inference in a fuzzy context: From theory to a virtual reality application," Computational Statistics & Data Analysis, Elsevier, vol. 56(4), pages 967-980.
    9. Pierpaolo D'Urso & Girish Prayag & Marta Disegna & Riccardo Massari, 2013. "Market Segmentation using Bagged Fuzzy C–Means (BFCM): Destination Image of Western Europe among Chinese Travellers," BEMPS - Bozen Economics & Management Paper Series BEMPS13, Faculty of Economics and Management at the Free University of Bozen.
    10. Gia Sirbiladze & Tariel Khvedelidze, 2023. "Associated Statistical Parameters’ Aggregations in Interactive MADM," Mathematics, MDPI, vol. 11(4), pages 1-17, February.
    11. Haoyu Liu & Kim Hua Tan & Xianfeng Wu, 2023. "Who’s watching? Classifying sports viewers on social live streaming services," Annals of Operations Research, Springer, vol. 325(1), pages 743-765, June.

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