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We present the results from a large near-infrared spectroscopic survey withSubaru/FMOS (\textit{FastSound}) consisting of $\sim$ 4,000 galaxies at$z\sim1.4$ with significant H$\alpha$ detection. We measure the gas-phasemetallicity from the [N~{\sc ii}]$\lambda$6583/H$\alpha$ emission line ratio ofthe composite spectra in various stellar mass and star-formation rate bins. Theresulting mass-metallicity relation generally agrees with previous studiesobtained in a similar redshift range to that of our sample. No clear dependenceof the mass-metallicity relation with star-formation rate is found. Our resultat $z\sim1.4$ is roughly in agreement with the fundamental metallicity relationat $z\sim0.1$ with fiber aperture corrected star-formation rate. We detectsignificant [S~{\sc ii}]$\lambda\lambda$6716,6731 emission lines from thecomposite spectra. The electron density estimated from the [S~{\scii}]$\lambda\lambda$6716,6731 line ratio ranges from 10 -- 500 cm$^{-3}$, whichgenerally agrees with that of local galaxies. On the other hand, thedistribution of our sample on [N~{\sc ii}]$\lambda$6583/H$\alpha$ vs. [S~{\scii}]$\lambda\lambda$6716,6731/H$\alpha$ is different from that found locally.We estimate the nitrogen-to-oxygen abundance ratio (N/O) from the N2S2 index,and find that the N/O in galaxies at $z\sim1.4$ is significantly higher thanthe local values at a fixed metallicity and stellar mass. The metallicity at$z\sim1.4$ recalculated with this N/O enhancement taken into account decreasesby 0.1 -- 0.2 dex. The resulting metallicity is lower than the localfundamental metallicity relation.

The Subaru FMOS Galaxy Redshift Survey (FastSound). III. The mass-metallicity relation and the fundamental metallicity relation at $z\sim1.4$