Fuzzy Clustering

  • Rudolf Kruse
  • Christian Borgelt
  • Frank Klawonn
  • Christian Moewes
  • Matthias Steinbrecher
  • Pascal Held
Part of the Texts in Computer Science book series (TCS)


After a brief overview of fuzzy methods in data analysis, this chapter focuses on fuzzy cluster analysis as the oldest fuzzy approach to data analysis. Fuzzy clustering comprises a family of prototype-based clustering methods that can be formulated as the problem of minimizing an objective function. These methods can be seen as “fuzzifications” of, for example, the classical c-means algorithm, which strives to minimize the sum of the (squared) distances between the data points and the cluster centers to which they are assigned. However, in order to “fuzzify” such a crisp clustering approach, it is not enough to merely allow values from the unit interval for the variables encoding the assignments of the data points to the clusters: the minimum is still obtained for a crisp data point assignment. As a consequence, additional means have to be employed in the objective function in order to obtain actual degrees of membership. This chapter surveys the most common fuzzification means and examines and compares their properties.


Objective Function Cluster Center Fuzzy Cluster Membership Degree Fuzzy Data 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag London 2013

Authors and Affiliations

  • Rudolf Kruse
    • 1
  • Christian Borgelt
    • 2
  • Frank Klawonn
    • 3
  • Christian Moewes
    • 1
  • Matthias Steinbrecher
    • 4
  • Pascal Held
    • 1
  1. 1.Faculty of Computer ScienceOtto-von-Guericke University MagdeburgMagdeburgGermany
  2. 2.Intelligent Data Analysis & Graphical Models Research UnitEuropean Centre for Soft ComputingMieresSpain
  3. 3.FB InformatikOstfalia University of Applied SciencesWolfenbüttelGermany
  4. 4.SAP Innovation CenterPotsdamGermany

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