  We present results of the classification of cloud structures toward the Orion
A Giant Molecular Cloud based on wide-field $^{12}$CO ($J$ = 1--0), $^{13}$CO
($J$ = 1-0), and C$^{18}$O ($J$ = 1-0) observations using the Nobeyama 45 m
radio telescope. We identified 78 clouds toward Orion A by applying Spectral
Clustering for Interstellar Molecular Emission Segmentation (SCIMES) to the
data cube of the column density of $^{13}$CO. Well-known subregions such as
OMC-1, OMC-2/3, OMC-4, OMC-5, NGC 1977, L1641-N, and the dark lane south
filament (DLSF) are naturally identified as distinct structures in Orion A.
These clouds can also be classified into three groups: the integral-shaped
filament, the southern regions of Orion A, and the other filamentary structures
in the outer parts of Orion A and the DLSF. These groups show differences in
scaling relations between the physical properties of the clouds. We derived the
abundance ratio between $^{13}$CO and C$^{18}$O,
$X_{^{13}\mathrm{CO}}/X_{\mathrm{C}^{18}\mathrm{O}}$, which ranges from 5.6 to
17.4 on median over the individual clouds. The significant variation of
$X_{^{13}\mathrm{CO}}/X_{\mathrm{C}^{18}\mathrm{O}}$ is also seen within a
cloud in both of the spatial and velocity directions and the ratio tends to be
high at the edge of the cloud. The values of
$X_{^{13}\mathrm{CO}}/X_{\mathrm{C}^{18}\mathrm{O}}$ decrease from 17 to 10
with the median of the column densities of the clouds at the column density of
$N_{\mathrm{C^{18}O}} \gtrsim 1 \times 10^{15}$ cm$^{-2}$ or visual extinction
of $A_V \gtrsim 3$ mag under the strong far-ultraviolet (FUV) environment of
$G_0 > 10^{3}$, whereas it is almost independent of the column density in the
weak FUV radiation field. These results are explained if the selective
photodissociation of C$^{18}$O is enhanced under a strong FUV environment and
it is suppressed in the dense part of the clouds.
