Abstract: The weighting exponent m is called the fuzzifier that
can have influence on the clustering performance of fuzzy c-means
(FCM) and mÎ[1.5,2.5] is suggested by Pal and Bezdek [13]. In this
paper, we will discuss the robust properties of FCM and show that the
parameter m will have influence on the robustness of FCM. According
to our analysis, we find that a large m value will make FCM more
robust to noise and outliers. However, if m is larger than the theoretical
upper bound proposed by Yu et al. [14], the sample mean will become
the unique optimizer. Here, we suggest to implement the FCM
algorithm with mÎ[1.5,4] under the restriction when m is smaller
than the theoretical upper bound.