Based on the article:
Land surface emissivity was calculated
using the NDVI threshold method [38] suggested by Beck et
al. [42]. The assumption is that bare has a NDVI < 0.2 [42].
The land surface is considered to be completely covered by
vegetation if NDVI > 0.5 [42]. When the NDVI values are
between 0.1 and 0.5 (0.1 β€ NDVI β€ 0.5), the land surface is
considered to be covered by vegetation and bare soil mixing.
As such, P_v is 0 at NDVI < 0.2, 1 at >0.5 and scaled inbetween (on a related note, the values used in this article were chosen for their location. Your location may require different values).
Calculating such a 'fractional vegetation cover' map is done using a linear regression and a raster calculator.