The fuzzy c-means algorithm (FCM) is one of widely used clustering algorithms.It is an open problem how to select an appropriate fuzziness index

m

when implementing the FCM.Some researchers have suggested that the best choice for

m

is probably in the interval based on their experimental results.In this paper

we discovered the theoretical connection between the validity of FCM algorithm as clustering algorithm and clustering validity

and pointed out that the weighting exponent

m

is not the optimal if it makes the FCM not to work properly as a clustering algorithm.According to this analysis

we carried on one experiment.The experimental result shows that the optimal weighting exponent in FCM algorithm could not always belong to the range .