  Two dimensional semiconductor such as single-layer transition metal
dichalcogenides (SL-TMD) have attracted most attentions as an atomically thin
layer semiconductor materials. Typically, lattice point defects (sulfur
vacancy) created by physical/chemical method during growth stages, have
disadvantages on electronic properties. However, photoluminescence (PL)
spectroscopy is conventionally used to characterize single-layer films but
until now it has not been used to show the presence of defects or estimate
their population due to overall similarity of general feature PL spectra. To
find a feasible and robust method to determine the presence of point defects on
single layer ${\rm MoS_2}$ without changing the experimental setup,
Multifractal Detrended Fluctuation Analysis (MF-DFA) and Multifractal Detrended
Moving Average Analysis (MF-DMA) are applied on the PL spectrum of single layer
${\rm MoS_2}$. We compare the scaling behavior of PL spectrum of pristine and
defective single layer ${\rm MoS_2}$ determined by MF-DFA and MF-DMA. Our
results reveal that PL spectrum has multifractal nature and different various
population of point defects (sulfur vacancy) on single layer ${\rm MoS_2}$
change dramatically multifractality characteristics (Hurst, H\"older exponents)
of photoluminescence spectrum. It is exhibited creating more lattice point
leads to smaller fluctuations in luminescent light that it can help to design
special defect structure for light emitted devices. The relative populations of
point defects are almost elucidated without utilizing expensive
characterization instruments such as scanning tunneling microscopy (STM) and
high resolution transmission electron microscopy (HR-TEM).
