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We introduce a new effective strategy to assign group and cluster membershipprobabilities $P_{mem}$ to galaxies using photometric redshift information.Large dynamical ranges both in halo mass and cosmic time are considered. Themethod takes the magnitude distribution of both cluster and field galaxies aswell as the radial distribution of galaxies in clusters into account using anon-parametric formalism and relies on Bayesian inference to take photometricredshift uncertainties into account. We successfully test the method against1,208 galaxy clusters within redshifts $z=0.05-2.58$ and masses$10^{13.29-14.80}~M_\odot$ drawn from wide field simulated galaxy mock catalogsdeveloped for the Euclid mission. Median purity $(55^{+17}_{-15})\%$ andcompleteness $(95^{+5}_{-10})\%$ are reached for galaxies brighter than0.25$L_\ast$ within $r_{200}$ of each simulated halo and for a statisticalphotometric redshift accuracy $\sigma((z_s-z_p)/(1+z_s))=0.03$. The mean values$p=56\%$ and $c=93\%$ have sub-percent uncertainties. Accurate photometricredshifts ($\sigma((z_s-z_p)/(1+z_s))\lesssim0.05$) and robust estimates forthe cluster redshift and the center coordinates are required. The method isapplied to derive accurate richness estimates. A statistical comparison betweenthe true ($N_{\rm true}$) vs estimated richness ($\lambda=\sum P_{mem}$) yieldson average to unbiased results, $Log(\lambda/N_{\rm true})=-0.0051\pm0.15$. Thescatter around the mean of the logarithmic difference between $\lambda$ and thehalo mass is 0.10~dex, for massive halos $\gtrsim10^{14.5}~M_\odot$. Ourestimates could be useful to calibrate independent cluster mass estimates fromweak lensing, SZ, and X-ray studies. Our method can be applied to any list ofgalaxy clusters or groups in both present and forthcoming surveys such as SDSS,CFHTLS, DES, LSST, and Euclid.

A new method to assign galaxy cluster membership using photometric redshifts