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For the fuzzy c-means algorithm described in this book, the sum of the membership degree of...

For the fuzzy c-means algorithm described in this book, the sum of the membership degree of any point over all clusters is 1. Instead, we could only require that the membership degree of a point in a cluster be between 0 and 1. What are the advantages and disadvantages of such an approach?

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Advantage-

It will have seperate membership degree 1,0 over each cluster and it would help us know the membership degree of a POINt in any particular cluster and not search in all the clusters and thus reduces the computing time as we have to traverse only the a particular cluster where the membership of the point is one instead of all the clusters.

Disadvantage-

The sum of membership degree can exceed 1 and if it is 1 ,it would require us to traverse through all clusters to find where the point has a membership and this increases computing time.

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