Partition validity and defuzzification

The fuzzy partition validity is a necessary measure to fix the number of gr oups in the fuzzy algorithms which need to know this data, We propose a mea sure based on the membership probabilities. Moreover, we propose a new conc ept of the hard partition based on the metric of the groups. The hard parti tion 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 har d partition, (C) 2000 Elsevier Science B.V. All rights reserved.