  In this paper, we take a new look at the possibilistic c-means (PCM) and
adaptive PCM (APCM) clustering algorithms from the perspective of uncertainty.
This new perspective offers us insights into the clustering process, and also
provides us greater degree of flexibility. We analyze the clustering behavior
of PCM-based algorithms and introduce parameters $\sigma_v$ and $\alpha$ to
characterize uncertainty of estimated bandwidth and noise level of the dataset
respectively. Then uncertainty (fuzziness) of membership values caused by
uncertainty of the estimated bandwidth parameter is modeled by a conditional
fuzzy set, which is a new formulation of the type-2 fuzzy set. Experiments show
that parameters $\sigma_v$ and $\alpha$ make the clustering process more easy
to control, and main features of PCM and APCM are unified in this new
clustering framework (UPCM). More specifically, UPCM reduces to PCM when we set
a small $\alpha$ or a large $\sigma_v$, and UPCM reduces to APCM when clusters
are confined in their physical clusters and possible cluster elimination are
ensured. Finally we present further researches of this paper.
