The derivation mistake of clustering center and the related wrong conclusion in Gao’s fuzzy maximum scatter difference discriminant criterion based clustering algorithm (FMSDCA) are pointed out.A new clustering algorithm based on fuzzy maximum scatter difference discriminant criterion (FMSDC)

called as fuzzy compactness and separation clustering algorithm based on fuzzy maximum scatter difference discriminant criterion (FMSDC-FCS)

is proposed.FMSDC-FCS make use of the FMSDC to generate optimal projection vector and make use of the fuzzy compactness and separation (FCS) algorithm to cluster the reduced-dimensional data set.The projection vector and clustering result are optimized by alternately running FMSDC in the original data space and FCS in the projection space

and the original data is clustered by clustering the reduced-dimensional data.The experimental results demonstrate that the overall performance of FMSDC-FCS surpasses that of original FCS algorithm

FMSDCA and classical fuzzy c-means algorithm.