We aim to study the statistical properties of dusty star-forming galaxies, such as their number counts, luminosity functions (LF) and dust-obscured star-formation rate density (SFRD). We use state-of-the-art de-blended Herschel catalogue in the COSMOS field, generated by combining the Bayesian source extraction tool XID+ and informative prior on the spectral energy distributions, to measure the number counts and LFs at far-infrared (FIR) and sub-millimetre (sub-mm) wavelengths. Thanks to our de-confusion technique and deep multi-wavelength photometry, we are able to achieve more accurate measurements while probing ten times below the confusion limit. Our number counts at 250 microns agree well with previous Herschel studies. However, our counts at 350 and 500 microns are considerably below previous Herschel results. This is due to previous studies suffering from source confusion which worsens towards longer wavelength. Our number counts at 450 and 870 microns show excellent agreement with previous determinations derived from single dish and interferometric observations. Our measurements of the monochromatic LF and the total IR LF agree well with previous results. The increased dynamic range of our measurements allows us to better measure the faint-end slope of the LF and measure the dust-obscured SFRD out to z~6. We find that the fraction of dust obscured star-formation activity is at its highest around z~1 which then decreases towards both low and high redshift. We do not find a shift of balance between z~3 and z~4 in the cosmic star-formation history from being dominated by unobscured star formation at higher redshift to obscured star formation at lower redshift. However, we do find 3<z<4 to be an interesting transition period as the fraction of the total SFRD that is obscured by dust is significantly lower at higher redshifts.
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