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The fuzzy partition validity is a necessary measure to fix the number of groups in the fuzzy algorithms which need to know this data. We propose a measure based on the membership probabilities. Moreover, we propose a new concept of the hard partition based on the metric of the groups. The hard partition can be obtained from the fuzzy partition, from which it is possible to find the hard membership...
A membership function and an objective function deduced from the geometrical properties associated to the metric defined by the covariance matrix of a sample have been proposed recently. We use these functions to determine the membership probabilities and the criterion function in the fuzzy C-means algorithm.
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