A Review of Cluster Validation with an Example of Type-2 Fuzzy Application in R

  • Ibrahim Ozkan
  • I. Burhan Türkşen
Part of the Studies in Fuzziness and Soft Computing book series (STUDFUZZ, volume 301)


Interval valued type-2 fuzziness can be represented by means of membership functions obtained with upper and lower values of the level of fuzziness. These upper and lower values for the level of fuzziness in FCM algorithm were obtained in our previous studies. A particular application of Interval valued type-2 fuzziness is shown for cluster validity analysis in this chapter. For this purpose, we introduce a brief taxonomy for cluster validity indices to clarify the contribution of our novel approach. To provide reproducibility of our technique, the source code is written in freely available language ‘R’ and can be found on our web site.


Cluster validity Internal criteria External criteria Relative criteria Stability type Biological type Compactness Connectedness Separation MiniMax ε-stable Partition coefficient Partition entropy Fukuyama-Sugeno Xie-Beni Dissimilarity Euclidian Manhattan Fuzzy c-mean Iris data R code Type 2 fuzzy Interval valued type-2 fuzzy Membership Upper and lower values of fuzziness Wine data 



This work was partially supported by the Natural Science and Engineering Research Council (NSERC) Grant (RPGIN 7698-05) to University of Toronto. Also, partial support is provided by Hacettepe University and TOBB Economics and Technology University. Their support is greatly appreciated.


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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.Department of EconomicsHacettepe UniversityAnkaraTurkey
  2. 2.TOBB ETUAnkaraTurkey
  3. 3.Department of Mechanical and Industrial EngineeringUniversity of TorontoOntarioCanada

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