The range of the value for the fuzzifier of the fuzzy c-means algorithm

The fuzzy c-means algorithm (FCM) is a widely used clustering algorithm. It is well known that the fuzzifier, m, which is also called fuzzy weighting exponent, has a significant impact on the performance of the FCM. Most of the researches have shown that there exists an effective range of the value for m. However, since the method adopted by researchers is mainly experimental or empirical, it is still an open problem how to select an appropriate fuzzifier m in theory when implementing the FCM. In this paper, we propose a theoretical approach to determine the range of the value of m. This approach utilizes the behavior of membership function on two data points, based on which we reveal the partial relationship between the fuzzifier m and the dataset structure.

► A theoretical approach used to determine the range of the value of m is proposed.
► The behavior of membership function on two special data points is analyzed.
► We set a threshold and obtain the range of the value.
► This range of the value is related with the number of cluster.
► The range of the value of m we find are close to those found by other researchers.