molecular hydrogen masses from the CO luminosity for 221 galaxies at 0 $< z <$ 2, then suggested that instead of the SFR, the third parameter that should be introduced into FMR is the gas mass.

The MZR and FMR are both established primarily using global galaxy parameters, it is also important to understand whether there is a more fundamental relation to probe the global MZR or FMR with local galactic parameters, e.g. stellar mass surface density, local metallicity, local SFR and local $D_{\rm n}4000$. The local metallicity vs. local stellar mass surface density relation has been investigated for years. @Edmunds1984a and @Vila-Costas1992a reported that ${\hbox{H\,{\sc ii}}}$ regions with larger stellar mass densities are more metal-rich than those with lower densities. [@Moran2012] performed long-slit spectroscopy on 174 star-forming galaxies and found a correlation between the local stellar mass surface density and metallicity, an analog to the global MZR. More recently, thanks to the emergence of the integral field spectroscopy (IFS) technique, analyzing these relations in a spatially resolved manner in relatively large samples of galaxies becomes feasible. @Rosales-Ortega2012 demonstrated the existence of a local relation between stellar mass surface density, metallicity, and SFR density using 38 nearby galaxies from the 