IDEAS home Printed from https://ideas.repec.org/a/eee/csdana/v56y2012i4p915-927.html
   My bibliography  Save this article

Fuzzy and possibilistic clustering for fuzzy data

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167947310003567
    Download Restriction: Full text for ScienceDirect subscribers only.
    File URL: https://libkey.io/10.1016/j.csda.2010.09.013?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Ferraro, Maria Brigida, 2024. "Fuzzy k-Means: history and applications," Econometrics and Statistics, Elsevier, vol. 30(C), pages 110-123.
    2. Fernando Reche & María Morales & Antonio Salmerón, 2020. "Statistical Parameters Based on Fuzzy Measures," Mathematics, MDPI, vol. 8(11), pages 1-20, November.
    3. 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.
    4. D'Urso, Pierpaolo & Disegna, Marta & Massari, Riccardo & Osti, Linda, 2016. "Fuzzy segmentation of postmodern tourists," Tourism Management, Elsevier, vol. 55(C), pages 297-308.
    5. 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.
    6. 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.
    7. 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.
    8. 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.
    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.
    12. 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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Colubi, Ana & Ramos-Guajardo, Ana Belén, 2023. "Fuzzy sets and (fuzzy) random sets in Econometrics and Statistics," Econometrics and Statistics, Elsevier, vol. 26(C), pages 84-98.
    2. Ferraro, Maria Brigida, 2024. "Fuzzy k-Means: history and applications," Econometrics and Statistics, Elsevier, vol. 30(C), pages 110-123.
    3. Doring, Christian & Lesot, Marie-Jeanne & Kruse, Rudolf, 2006. "Data analysis with fuzzy clustering methods," Computational Statistics & Data Analysis, Elsevier, vol. 51(1), pages 192-214, November.
    4. 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.
    5. D'Urso, Pierpaolo & Santoro, Adriana, 2006. "Fuzzy clusterwise linear regression analysis with symmetrical fuzzy output variable," Computational Statistics & Data Analysis, Elsevier, vol. 51(1), pages 287-313, November.
    6. Ana Colubi & Renato Coppi & Pierpaolo D’urso & Maria angeles Gil, 2007. "Statistics with fuzzy random variables," Metron - International Journal of Statistics, Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome, vol. 0(3), pages 277-303.
    7. Pierpaolo D’Urso & Livia Giovanni & Marta Disegna & Riccardo Massari & Vincenzina Vitale, 2021. "A Tourist Segmentation Based on Motivation, Satisfaction and Prior Knowledge with a Socio-Economic Profiling: A Clustering Approach with Mixed Information," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 154(1), pages 335-360, February.
    8. Giordani, Paolo, 2010. "Three-way analysis of imprecise data," Journal of Multivariate Analysis, Elsevier, vol. 101(3), pages 568-582, March.
    9. D'Urso, Pierpaolo & Disegna, Marta & Massari, Riccardo & Osti, Linda, 2016. "Fuzzy segmentation of postmodern tourists," Tourism Management, Elsevier, vol. 55(C), pages 297-308.
    10. Pierpaolo D'Urso & Paolo Giordani, 2006. "A robust fuzzy k-means clustering model for interval valued data," Computational Statistics, Springer, vol. 21(2), pages 251-269, June.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:csdana:v:56:y:2012:i:4:p:915-927. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/csda .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.