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We introduce ($\alpha,\beta,\gamma$) weighted Wigner-Yanase-Dyson(($\alpha,\beta,\gamma$) WWYD) skew information and ($\alpha,\beta,\gamma$)modified weighted Wigner-Yanase-Dyson (($\alpha,\beta,\gamma$) MWWYD) skewinformation. We explore the sum uncertainty relations for arbitrary $N$mutually noncommutative observables based on ($\alpha,\beta,\gamma$) WWYD skewinformation. A series of uncertainty inequalities are derived. We show bydetailed example that our results cover and improve the previous ones based onthe original Wigner-Yanase (WY) skew information. Finally, we establish new sumuncertainty relations in terms of the ($\alpha,\beta,\gamma$) MWWYD skewinformation for arbitrary $N$ quantum channels.

Sum uncertainty relations based on $(\alpha,\beta,\gamma)$ weighted Wigner-Yanase-Dyson skew information