Linguistic Possibilistic C-Means (LPCM)

Linguistic Possibilistic C-Means (LPCM) is an extended version of the Possibilistic C-Means based on the extension principle and the decomposition theory. The input vectors are vectors of fuzzy subsets. The LPCM categorizes input vectors with similar characteristics into the same group. The membership function of an input vectors to each cluster is a fuzzy subset. It is not relative and depends only on the distance of an input from cluster center rather than on the distance of an input from all other cluster centers. The LPCM has an ability to handle noise points, i.e., noise points have low membership in all cluster.

Example

Cluster centers produced by the LPCM Membership function of one of noise

Membership function of another noise