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Gamma-ray bursts (GRBs) are widely believed to be from massive collapsars and/or compact binary mergers, which accordingly, would generate long and short GRBs, respectively. The details on this classification scheme have been in constant debate given more and more observational data available to us. In this work, we apply a series of data mining methods to studying the potential classification information contained in the prompt emission of GRBs detected by the Fermi Gamma-ray Burst Monitor. A tight global correlation is found between fluence ($f$), peak flux ($F$) and prompt duration ($T_{90}$) which takes the form of $ \log {\it f}= 0.75 \log T_{90} +0.92 \log F -7.14$. Based on this correlation, we can define a new parameter $L = 1.66\log T_{90} + 0.84 \log {\it f} - 0.46 \log F + 3.24$ by linear discriminant analysis that would distinguish between long and short GRBs with much less ambiguity than $T_{90}$. We also discussed the three subclasses scheme of GRB classification derived from clusters analysis based on a Gaussian mixture model, and suggest that, besides SGRBs, LGRBs may be divided into long-bright gamma-ray bursts (LBGRBs) and long-faint gamma-ray bursts (LFGRBs), LBGRBs have statistical higher $f$ and $F$ than LFGRBs; further statistical analysis found that LBGRBs also have higher number of GRB pulses than LFGRBs.