If NDVI values are lower that 0 (-0.1 to -1) we have water bodies. The emissivity value for water is 0.995.
So, I think that the NDVI threshold should look like this:
if NDVI is under 0 (negative values), then we have water > emissivity for water is 0.995
if NDVI is between 0 and 0.2, then we have bare soil > emissivity for bare soil is 0.97
if NDVI is > 0.5, then we have vegetation > emissivity for vegetation is 0.99
if NDVI is between the values 0.2 and 0.5 ( 0.2 ≤ NDVI ≤ 0.5), then we have a mixture of bare soil and vegetation > emissivity is calculated by the equation of Sobrino method