Introduction to statistical pattern recognition (2nd ed.)
Introduction to statistical pattern recognition (2nd ed.)
A local geometrical properties application to fuzzy clustering
Fuzzy Sets and Systems
Membership functions in the fuzzy C-means algorithm
Fuzzy Sets and Systems
Similarity relations and fuzzy orderings
Information Sciences: an International Journal
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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 probabilities and the hard partition validity. A similarity relation is proposed over the set of groups belonging to the hard partition.