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The value range of fuzzy weighting exponent m is larger than 1 in the possibilistic C-means clustering (PCM). Through analysis and discussion on the PCM algorithm, we set the weighting exponent m as multiple independent variables, and extend the value ranges of the weighting exponents, thus obtaining a new clustering algorithm, named general possibilistic C-means clustering (GPCM). The new value scope of the GPCM's weighting exponents is proved theoretically, and the fuzzy membership of the samples is estimated by the particle swarm optimization (PSO) algorithm. The GPCM algorithm breaks the restriction of the PCM on parameter m, and simulation results demonstrate its effectiveness. [ABSTRACT FROM AUTHOR]