MiniMax ε-stable cluster validity index for Type-2 fuzziness

Authors:
Ibrahim Ozkan;I. Burhan Türkşen
Affiliations:
Department of Economics, Hacettepe Univ., Ankara, Turkey;Department of Industrial Engineering, TOBB ETU, Ankara, Turkey and Department of Mechanical and Industrial Engineering, University of Toronto, Ontario, Canada M5S 3G8
Venue:
Information Sciences: an International Journal
Year:
2012

Citing 28
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Abstract

In this paper, we concentrate on the usage of uncertainty associated with the level of fuzziness in determination of the number of clusters in FCM for any data set. We propose a MiniMax @e-stable cluster validity index based on the uncertainty associated with the level of fuzziness within the framework of interval valued Type 2 fuzziness. If the data have a clustered structure, the optimum number of clusters may be assumed to have minimum uncertainty under upper and lower levels of fuzziness. Upper and lower values of the level of fuzziness for Fuzzy C-Mean (FCM) clustering methodology have been found as m=2.6 and 1.4, respectively, in our previous studies. Our investigation shows that the stability of cluster centers with respect to the level of fuzziness is sufficient for the determination of the number of clusters.