I
AE
S In
t
er
na
t
io
na
l J
o
urna
l o
f
Art
if
icia
l In
t
ellig
ence
(
I
J
-
AI
)
Vo
l.
15
,
No
.
4
,
A
u
g
u
s
t 2
0
2
6
,
p
p
.
3
2
8
6
~
3
2
9
8
I
SS
N:
2
2
5
2
-
8
9
3
8
,
DOI
: 1
0
.
1
1
5
9
1
/ijai.v
15
.i
4
.
p
p
3
2
8
6
-
3
2
9
8
3286
J
o
ur
na
l ho
m
ep
a
g
e
:
h
ttp
:
//ij
a
i
.
ia
esco
r
e.
co
m
Dete
rmi
ning
stud
ent
sca
f
folding
le
v
els in geo
metry
pro
blem
-
so
lv
ing
:
a
f
uzzy
i
nferenc
e sy
stem
u
sing
Ma
mda
ni method
Yuni
a
r
I
k
a
P
utr
i P
ra
ny
a
t
a
1,
2
,
Su
s
is
wo
1
,
T
j
a
ng
Da
niel Ch
a
nd
ra
1
1
D
e
p
a
r
t
me
n
t
o
f
M
a
t
h
e
m
a
t
i
c
s
,
F
a
c
u
l
t
y
o
f
M
a
t
h
e
mat
i
c
s
a
n
d
N
a
t
u
r
a
l
S
c
i
e
n
c
e
s
,
U
n
i
v
e
r
s
i
t
a
s Ne
g
e
r
i
M
a
l
a
n
g
,
M
a
l
a
n
g
,
I
n
d
o
n
e
si
a
2
M
a
t
h
e
ma
t
i
c
s E
d
u
c
a
t
i
o
n
S
t
u
d
y
P
r
o
g
r
a
m,
F
a
c
u
l
t
y
o
f
S
c
i
e
n
c
e
a
n
d
T
e
c
h
n
o
l
o
g
y
,
U
n
i
v
e
r
s
i
t
a
s PG
R
I
K
a
n
j
u
r
u
h
a
n
M
a
l
a
n
g
,
M
a
l
a
n
g
,
I
n
d
o
n
e
s
i
a
Art
icle
I
nfo
AB
S
T
RAC
T
A
r
ticle
his
to
r
y:
R
ec
eiv
ed
Au
g
1
3
,
2
0
2
4
R
ev
is
ed
J
u
n
1
0
,
2
0
2
6
Acc
ep
ted
J
u
l 9
,
2
0
2
6
Th
is
st
u
d
y
a
ims
t
o
a
d
o
p
t
a
fu
z
z
y
lo
g
ic
in
fe
re
n
c
e
sy
ste
m
u
sin
g
M
a
m
d
a
n
i
m
e
th
o
d
t
o
d
e
term
in
e
th
e
a
p
p
ro
p
r
iate
sc
a
ffo
ld
in
g
lev
e
l
f
o
r
stu
d
e
n
ts
b
a
se
d
o
n
e
rro
rs
in
so
lv
i
n
g
g
e
o
m
e
try
p
r
o
b
lem
s.
Th
e
fu
z
z
y
in
fe
re
n
c
e
sy
ste
m
(F
IS
)
a
ss
e
ss
e
d
th
e
st
u
d
e
n
ts'
u
n
d
e
rsta
n
d
in
g
a
n
d
p
r
o
v
i
d
e
d
sc
a
ffo
ld
i
n
g
t
o
a
d
d
re
ss
sp
e
c
ifi
c
lea
rn
in
g
n
e
e
d
s
b
y
a
n
a
ly
z
in
g
c
o
m
m
o
n
m
istak
e
s
in
g
e
o
m
e
try
p
ro
b
lem
-
so
lv
i
n
g
.
Th
is
m
e
th
o
d
o
p
ti
m
ize
d
th
e
e
d
u
c
a
ti
o
n
a
l
p
r
o
c
e
ss
b
y
o
ffe
ri
n
g
p
e
rso
n
a
li
z
e
d
s
u
p
p
o
rt
,
e
n
h
a
n
c
in
g
stu
d
e
n
ts'
p
ro
b
lem
-
so
lv
i
n
g
s
k
il
ls,
a
n
d
re
d
u
c
in
g
e
rro
r
ra
tes
.
T
h
e
d
a
ta
p
ro
c
e
ss
in
g
c
rit
e
ria
u
si
n
g
t
h
e
F
IS
in
v
o
lv
e
d
a
n
a
ly
z
in
g
t
h
e
sc
o
re
s
o
f
m
a
th
e
m
a
ti
c
s
e
d
u
c
a
ti
o
n
stu
d
e
n
ts
a
t
a
p
r
iv
a
te
u
n
i
v
e
rsity
i
n
M
a
lan
g
wh
e
n
s
o
lv
in
g
g
e
o
m
e
try
p
ro
b
lem
s,
b
a
se
d
o
n
P
ó
l
y
a
'
s
sta
g
e
s.
M
a
m
d
a
n
i
wa
s
u
se
d
to
p
r
o
v
i
d
e
re
c
o
m
m
e
n
d
a
ti
o
n
s
b
a
se
d
o
n
stu
d
e
n
ts'
c
o
g
n
i
ti
v
e
d
a
ta
wh
il
e
s
o
lv
in
g
g
e
o
m
e
try
p
r
o
b
lem
s,
in
li
n
e
wi
th
s
c
a
ffo
ld
in
g
c
o
m
p
o
n
e
n
ts.
Th
e
re
su
lt
s
sh
o
we
d
th
a
t
th
e
sy
ste
m
p
e
rso
n
a
li
z
e
d
sc
a
ffo
ld
i
n
g
lev
e
ls
fo
r
st
u
d
e
n
ts
w
o
rk
i
n
g
o
n
g
e
o
m
e
try
p
r
o
b
lem
s.
T
h
is
c
o
n
tri
b
u
ted
to
th
e
field
o
f
e
d
u
c
a
ti
o
n
a
l
tec
h
n
o
l
o
g
y
b
y
p
re
se
n
ti
n
g
a
n
e
w
a
p
p
r
o
a
c
h
t
o
a
d
a
p
ti
v
e
lea
rn
in
g
a
n
d
e
m
p
h
a
siz
e
d
th
e
imp
o
rtan
c
e
o
f
p
e
rso
n
a
li
z
e
d
p
e
d
a
g
o
g
ica
l
su
p
p
o
rt.
Th
e
a
p
p
ro
a
c
h
wa
s
p
a
rt
icu
larly
b
e
n
e
ficia
l
fo
r
g
e
o
m
e
try
tea
c
h
e
rs
wh
o
p
ro
v
id
e
d
in
d
iv
i
d
u
a
li
z
e
d
sc
a
ffo
l
d
i
n
g
b
a
se
d
o
n
st
u
d
e
n
ts'
e
rro
rs,
c
o
n
t
rib
u
ti
n
g
to
imp
ro
v
e
d
lea
rn
i
n
g
o
u
tc
o
m
e
s.
K
ey
w
o
r
d
s
:
E
r
r
o
r
a
n
aly
s
is
Fu
zz
y
in
f
er
e
n
ce
s
y
s
tem
Geo
m
etr
y
p
r
o
b
lem
s
o
lv
i
n
g
Ma
m
d
an
i m
eth
o
d
Stu
d
en
t scaf
f
o
ld
in
g
T
h
is i
s
a
n
o
p
e
n
a
c
c
e
ss
a
rticle
u
n
d
e
r th
e
CC B
Y
-
SA
li
c
e
n
se
.
C
o
r
r
e
s
p
o
nd
ing
A
uth
o
r
:
Su
s
is
wo
Dep
ar
tm
en
t
o
f
Ma
th
em
atics,
Facu
lty
o
f
Ma
th
e
m
atics a
n
d
Na
tu
r
al
Scien
ce
s
,
Un
iv
er
s
itas
Neg
er
i M
alan
g
St.
Sem
ar
an
g
No
.
5
,
Ma
lan
g
,
I
n
d
o
n
esia
E
m
ail:
s
u
s
is
wo
.
f
m
ip
a@
u
m
.
ac
.
id
1.
I
NT
RO
D
UCT
I
O
N
Geo
m
etr
y
is
a
co
r
e
ar
ea
o
f
m
ath
em
atics
th
at
p
lay
s
a
cr
u
cial
r
o
le
in
d
ev
elo
p
in
g
s
tu
d
en
ts
'
m
ath
em
atica
l
th
in
k
in
g
.
Desp
it
e
th
e
u
n
d
e
n
iab
le
s
ig
n
if
ican
c
e,
th
is
co
n
ce
p
t
r
em
ai
n
s
a
c
h
allen
g
in
g
to
p
ic
an
d
is
o
f
ten
p
e
r
ce
iv
ed
as
d
i
f
f
icu
lt
b
y
m
an
y
s
tu
d
e
n
ts
at
d
if
f
er
e
n
t
lev
els
o
f
ed
u
ca
tio
n
[
1
]
.
T
h
e
d
if
f
i
cu
lties
ar
e
n
o
t
o
n
ly
lim
ited
to
u
n
d
e
r
s
tan
d
in
g
b
asic
co
n
ce
p
ts
,
b
u
t
ex
ten
d
to
th
e
ap
p
licatio
n
o
f
g
e
o
m
etr
y
i
n
p
r
o
b
lem
s
o
lv
in
g
an
d
s
p
atial
r
ea
s
o
n
in
g
.
R
ec
en
t
s
tu
d
i
es
s
u
g
g
est
th
at
ch
allen
g
es
in
l
ea
r
n
in
g
g
eo
m
et
r
y
ca
n
r
esu
lt f
r
o
m
v
a
r
io
u
s
f
ac
t
o
r
s
,
in
clu
d
in
g
co
n
c
ep
tu
al
c
o
m
p
le
x
ity
,
th
e
n
ee
d
f
o
r
s
tr
o
n
g
v
is
u
al
izatio
n
,
an
d
th
e
r
elatio
n
s
h
ip
b
etwe
en
g
eo
m
et
r
ic
an
d
alg
eb
r
aic
r
ep
r
esen
tatio
n
s
[
2
]
,
[
3
]
.
A
v
ar
iety
o
f
in
n
o
v
ativ
e
s
tr
ateg
ies
an
d
a
p
p
r
o
ac
h
es
h
av
e
b
ee
n
d
ev
el
o
p
ed
to
a
d
d
r
ess
th
e
c
h
allen
g
es
o
f
lear
n
in
g
g
eo
m
etr
y
.
An
im
p
o
r
tan
t
s
tr
ateg
y
p
r
o
v
e
n
ef
f
ec
tiv
e
is
th
e
u
s
e
o
f
s
ca
f
f
o
ld
in
g
,
wh
ich
p
r
o
v
id
es
s
tr
u
ctu
r
ed
s
u
p
p
o
r
t
to
s
tu
d
en
ts
in
b
u
ild
in
g
g
e
o
m
etr
ic
u
n
d
e
r
s
tan
d
in
g
[
4
]
,
[
5
]
.
Scaf
f
o
ld
in
g
in
g
eo
m
etr
y
lear
n
in
g
ca
n
tak
e
v
ar
io
u
s
f
o
r
m
s
,
s
p
a
n
n
in
g
f
r
o
m
v
e
r
b
al
in
s
tr
u
ctio
n
s
to
d
ig
ital
v
is
u
aliza
tio
n
to
o
ls
.
Ho
wev
er
,
th
e
d
eter
m
in
atio
n
o
f
t
h
e
ap
p
r
o
p
r
i
ate
lev
el
an
d
ty
p
e
o
f
s
ca
f
f
o
l
d
in
g
r
e
m
ain
s
a
c
h
allen
g
e,
g
i
v
en
th
e
d
iv
er
s
ity
o
f
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Ar
tif
I
n
tell
I
SS
N:
2252
-
8
9
3
8
Dete
r
min
in
g
s
tu
d
en
t sca
ffo
ld
in
g
leve
ls
in
g
eo
metry
p
r
o
b
lem
-
s
o
lvin
g
:
a
f
u
z
z
y
…
(
Yu
n
ia
r
I
k
a
P
u
tr
i P
r
a
n
ya
ta
)
3287
s
tu
d
en
ts
'
ab
ilit
ie
s
,
lear
n
in
g
s
ty
les,
an
d
in
d
iv
id
u
al
n
ee
d
s
[
6
]
–
[
8
]
.
A
m
o
r
e
s
y
s
tem
atic
an
d
a
d
ap
tiv
e
ap
p
r
o
ac
h
in
d
eter
m
in
in
g
t
h
e
lev
el
is
n
ee
d
e
d
to
o
p
tim
ize
t
h
e
g
eo
m
etr
y
lea
r
n
in
g
p
r
o
ce
s
s
.
T
h
e
d
ev
elo
p
m
en
t
o
f
d
ig
ital
te
ch
n
o
lo
g
y
h
as
o
p
en
ed
u
p
n
ew
o
p
p
o
r
tu
n
ities
in
g
eo
m
etr
y
le
ar
n
in
g
a
n
d
th
e
ap
p
licatio
n
o
f
m
o
r
e
ad
ap
t
iv
e
s
ca
f
f
o
ld
in
g
.
T
h
e
f
u
zz
y
in
f
er
en
ce
s
y
s
tem
(
FIS)
u
s
in
g
th
e
Ma
m
d
an
i
m
et
h
o
d
p
r
o
v
id
es
a
p
r
o
m
is
in
g
way
t
o
h
an
d
le
th
e
co
m
p
lex
ity
o
f
f
in
d
in
g
th
e
o
p
tim
al
lev
el
i
n
g
e
o
m
etr
y
lear
n
in
g
.
FIS
h
an
d
les
u
n
ce
r
tain
ty
an
d
am
b
ig
u
ity
in
th
e
ass
ess
m
en
t
o
f
s
tu
d
en
t
er
r
o
r
r
ates
a
n
d
p
r
o
d
u
ce
s
m
o
r
e
f
lex
i
b
le
an
d
ad
ap
tiv
e
d
ec
is
io
n
s
th
a
n
co
n
v
e
n
tio
n
al
r
u
le
-
b
ased
s
y
s
tem
s
[
9
]
,
[
1
0
]
.
T
h
e
ap
p
licatio
n
in
m
at
h
em
atics
ed
u
ca
tio
n
h
as
s
h
o
wn
p
o
s
itiv
e
r
esu
lts
in
a
v
ar
iety
o
f
co
n
te
x
ts
,
in
clu
d
in
g
ass
es
s
m
en
t
o
f
s
tu
d
en
t
p
er
f
o
r
m
an
ce
,
ad
ap
tatio
n
o
f
lear
n
in
g
m
ater
ials
,
an
d
p
er
s
o
n
aliza
tio
n
o
f
th
e
lear
n
i
n
g
ex
p
er
ien
ce
[
1
1
]
.
T
h
is
s
tu
d
y
aim
s
to
d
ev
elo
p
a
FIS
u
s
in
g
th
e
Ma
m
d
an
i
m
eth
o
d
to
d
ete
r
m
in
e
th
e
a
p
p
r
o
p
r
iate
s
ca
f
f
o
ld
in
g
le
v
el
f
o
r
s
tu
d
en
ts
,
b
ased
o
n
t
h
eir
er
r
o
r
s
in
s
o
lv
in
g
g
eo
m
et
r
y
p
r
o
b
lem
s
.
T
h
e
s
y
s
tem
is
ex
p
ec
ted
t
o
ass
is
t
teac
h
er
s
in
p
r
o
v
i
d
in
g
m
o
r
e
tar
g
ete
d
an
d
ef
f
ec
tiv
e
s
u
p
p
o
r
t
to
s
tu
d
en
ts
to
im
p
r
o
v
e
u
n
d
er
s
tan
d
in
g
a
n
d
p
er
f
o
r
m
an
ce
in
lear
n
in
g
g
eo
m
etr
y
[
1
]
,
[
1
2
]
.
T
h
e
g
ap
b
et
wee
n
th
eo
r
y
an
d
p
r
ac
tice
is
b
r
id
g
ed
b
y
in
te
g
r
atin
g
k
n
o
wled
g
e
ab
o
u
t
ty
p
es o
f
er
r
o
r
s
[
1
3
]
,
[
1
4
]
an
d
p
r
in
ci
p
les o
f
ef
f
ec
tiv
e
s
ca
f
f
o
ld
in
g
[
6
]
,
[
1
5
]
.
I
n
th
e
co
n
tex
t
o
f
g
eo
m
et
r
y
lear
n
in
g
,
FIS
is
u
s
ed
to
an
aly
z
e
th
e
d
if
f
er
e
n
t
ty
p
es
o
f
er
r
o
r
s
s
tu
d
en
ts
m
ak
e
an
d
r
ec
o
m
m
en
d
ap
p
r
o
p
r
iate
lev
els
o
f
s
ca
f
f
o
ld
in
g
.
R
ec
en
t
s
tu
d
ies
h
av
e
id
en
ti
f
ied
s
ev
er
al
m
ajo
r
ca
teg
o
r
ies
o
f
er
r
o
r
s
in
g
eo
m
etr
y
,
in
clu
d
i
n
g
c
o
n
ce
p
tu
al,
p
r
o
ce
d
u
r
al,
a
n
d
v
is
u
al
-
s
p
atial
er
r
o
r
s
[
1
4
]
–
[
1
8
]
.
I
n
co
n
s
id
er
in
g
th
e
e
r
r
o
r
c
h
ar
ac
t
er
is
tics
,
FIS
s
y
s
tem
s
ar
e
d
e
s
ig
n
ed
to
p
r
o
v
id
e
m
o
r
e
tar
g
eted
an
d
ef
f
ec
tiv
e
s
ca
f
f
o
ld
in
g
r
ec
o
m
m
e
n
d
atio
n
s
,
h
elp
in
g
s
tu
d
e
n
ts
o
v
er
c
o
m
e
s
p
ec
if
ic
b
ar
r
ier
s
in
g
e
o
m
etr
y
u
n
d
er
s
tan
d
in
g
.
T
h
e
d
ev
elo
p
m
en
t
o
f
FIS
-
b
ased
s
ca
f
f
o
ld
in
g
s
y
s
tem
s
f
o
r
g
eo
m
etr
y
lear
n
in
g
r
eq
u
i
r
es
ca
r
ef
u
l
in
teg
r
atio
n
o
f
lear
n
in
g
t
h
eo
r
y
,
g
eo
m
etr
y
d
o
m
ain
k
n
o
wled
g
e,
an
d
i
n
tellig
en
t
s
y
s
tem
d
esig
n
p
r
in
cip
les.
T
h
is
in
ter
d
is
cip
lin
ar
y
ap
p
r
o
ac
h
in
clu
d
es
an
in
-
d
ep
th
an
al
y
s
is
o
f
s
tu
d
en
ts
'
co
g
n
itiv
e
p
r
o
ce
s
s
es
in
g
eo
m
etr
y
lear
n
in
g
,
an
u
n
d
er
s
tan
d
in
g
o
f
th
e
s
tr
u
ctu
r
e
an
d
r
elatio
n
s
h
i
p
s
o
f
g
eo
m
et
r
ic
co
n
ce
p
ts
,
an
d
co
n
s
id
er
atio
n
o
f
p
ed
ag
o
g
ical
asp
ec
ts
in
th
e
ap
p
licatio
n
o
f
s
ca
f
f
o
ld
in
g
[
1
9
]
–
[
2
2
]
.
Fu
r
th
er
m
o
r
e,
th
e
d
esig
n
s
h
o
u
ld
also
co
n
s
id
er
th
e
p
r
ac
tical
asp
ec
ts
o
f
im
p
le
m
en
tatio
n
i
n
ac
tu
al
class
r
o
o
m
en
v
ir
o
n
m
e
n
ts
,
in
clu
d
i
n
g
ea
s
e
o
f
u
s
e
f
o
r
teac
h
er
s
an
d
s
tu
d
en
ts
,
as we
ll a
s
th
e
ab
ilit
y
to
in
teg
r
ate
with
ex
is
tin
g
lear
n
in
g
s
y
s
tem
s
.
E
v
alu
atin
g
th
e
ef
f
ec
tiv
e
n
ess
o
f
FIS
-
b
ased
s
ca
f
f
o
ld
in
g
s
y
s
t
em
s
in
lear
n
in
g
g
eo
m
etr
y
is
a
cr
u
cial
asp
ec
t
th
at
r
eq
u
ir
es
a
r
ig
o
r
o
u
s
m
eth
o
d
o
lo
g
ical
ap
p
r
o
ac
h
.
R
e
ce
n
t
s
tu
d
ies
h
av
e
s
h
o
wn
th
e
i
m
p
o
r
tan
ce
o
f
u
s
in
g
m
ix
ed
m
eth
o
d
s
th
at
co
m
b
i
n
e
q
u
an
titativ
e
an
d
q
u
alitativ
e
a
n
aly
s
is
to
u
n
d
er
s
tan
d
t
h
e
im
p
ac
t
o
f
m
ath
em
atics
lear
n
in
g
in
te
r
v
en
tio
n
s
[
5
]
,
[
2
1
]
.
I
n
th
e
co
n
tex
t
o
f
s
ca
f
f
o
l
d
in
g
s
y
s
tem
s
f
o
r
g
eo
m
etr
y
,
ev
alu
a
tio
n
s
h
o
u
ld
in
clu
d
e
im
p
r
o
v
em
e
n
ts
in
s
tu
d
en
t
p
er
f
o
r
m
an
ce
,
ch
an
g
es
in
attitu
d
es
to
war
d
g
e
o
m
etr
y
,
d
ev
el
o
p
m
e
n
t
o
f
m
etac
o
g
n
itiv
e
s
k
ills
,
an
d
tr
an
s
f
er
o
f
u
n
d
er
s
tan
d
in
g
t
o
o
th
er
m
ath
em
atica
l d
o
m
ain
s
.
T
h
e
im
p
lem
en
tatio
n
o
f
FIS
-
b
ased
s
ca
f
f
o
ld
in
g
s
y
s
tem
s
m
u
s
t
co
n
s
id
er
th
e
s
o
cial
an
d
cu
ltu
r
al
co
n
tex
t
o
f
lear
n
in
g
.
R
ec
en
t
s
tu
d
ies
e
m
p
h
asize
th
e
im
p
o
r
tan
ce
o
f
cu
ltu
r
ally
r
esp
o
n
s
iv
e
a
p
p
r
o
ac
h
es
in
m
at
h
em
atics
ed
u
ca
tio
n
,
in
clu
d
in
g
g
eo
m
et
r
y
[
2
3
]
–
[
2
5
]
.
T
h
e
s
ca
f
f
o
l
d
in
g
s
y
s
tem
s
h
o
u
ld
b
e
s
u
f
f
i
cien
tly
f
lex
ib
le
t
o
ac
co
m
m
o
d
ate
v
ar
io
u
s
p
er
s
p
e
ctiv
es
an
d
ex
p
e
r
ien
ce
s
o
f
s
tu
d
en
ts
as
well
as
s
u
p
p
o
r
t
th
e
d
ev
elo
p
m
en
t
o
f
a
p
o
s
itiv
e
m
ath
em
atica
l id
en
tity
.
T
h
e
an
aly
s
is
o
f
er
r
o
r
s
in
g
e
o
m
etr
y
p
r
o
b
lem
s
o
lv
in
g
ca
n
b
e
en
h
a
n
ce
d
b
y
ap
p
ly
i
n
g
Pó
ly
a'
s
p
r
o
b
lem
s
o
lv
in
g
f
r
am
ewo
r
k
,
wh
ich
in
c
lu
d
es
f
o
u
r
s
tag
es:
u
n
d
er
s
tan
d
i
n
g
th
e
p
r
o
b
le
m
,
p
lan
n
in
g
th
e
s
o
lu
tio
n
,
ex
ec
u
tin
g
th
e
p
lan
,
an
d
ch
ec
k
in
g
b
ac
k
[
2
6
]
.
R
ec
en
t
s
tu
d
ies
s
h
o
w
th
at
in
teg
r
atin
g
Pó
ly
a'
s
s
tag
es
wit
h
er
r
o
r
an
aly
s
is
ca
n
p
r
o
v
id
e
d
ee
p
er
in
s
ig
h
ts
in
to
d
if
f
icu
lties
in
g
eo
m
etr
y
[
2
7
]
–
[
2
9
]
.
At
th
e
p
r
o
b
lem
u
n
d
er
s
tan
d
in
g
s
tag
e,
s
tu
d
en
ts
o
f
ten
h
av
e
d
if
f
icu
lty
in
ter
p
r
etin
g
th
e
g
iv
en
g
e
o
m
etr
ic
in
f
o
r
m
atio
n
a
n
d
id
en
tif
y
in
g
k
e
y
elem
en
ts
o
f
th
e
p
r
o
b
lem
[
3
0
]
.
I
n
th
e
p
lan
n
in
g
th
e
s
o
lu
tio
n
s
tag
e,
er
r
o
r
s
o
f
ten
o
cc
u
r
wh
en
th
er
e
is
f
ailu
r
e
to
co
n
n
ec
t
r
elev
a
n
t
g
eo
m
etr
ic
c
o
n
ce
p
ts
o
r
c
h
o
o
s
e
in
ap
p
r
o
p
r
iate
s
tr
ateg
ies
[
3
1
]
.
Du
r
in
g
t
h
e
ex
ec
u
tio
n
o
f
th
e
p
lan
,
p
r
o
ce
d
u
r
al
an
d
ca
lcu
latio
n
er
r
o
r
s
o
f
ten
a
p
p
ea
r
,
s
p
ec
if
ically
wh
en
s
tu
d
e
n
ts
ap
p
ly
g
e
o
m
etr
y
f
o
r
m
u
las
o
r
th
eo
r
em
s
[
3
2
]
.
At
th
e
r
e
ch
ec
k
s
ta
g
e
,
m
a
n
y
s
t
u
d
en
ts
f
ail
t
o
p
e
r
f
o
r
m
ad
e
q
u
ate
v
e
r
i
f
ic
ati
o
n
o
r
a
r
e
u
n
a
b
le
t
o
i
d
e
n
ti
f
y
er
r
o
r
s
i
n
s
o
l
u
t
io
n
s
.
T
h
e
in
teg
r
atio
n
o
f
Po
ly
a
s
tag
e
-
b
ased
e
r
r
o
r
an
al
y
s
is
in
to
FIS
s
ca
f
f
o
ld
in
g
s
y
s
tem
s
in
cr
ea
s
es
th
e
p
r
ec
is
io
n
an
d
ef
f
ec
tiv
e
n
ess
o
f
s
u
p
p
o
r
t.
T
h
e
s
y
s
tem
p
r
o
v
i
d
es
m
o
r
e
tar
g
eted
an
d
co
n
tex
tu
al
ized
s
ca
f
f
o
ld
in
g
b
y
id
en
tify
in
g
at
w
h
ich
s
tag
e
s
tu
d
en
ts
ar
e
h
av
i
n
g
d
if
f
icu
lty
[
6
]
.
Fo
r
ex
am
p
le,
wh
en
a
s
tu
d
en
t h
as
d
if
f
icu
lty
at
th
e
p
r
o
b
lem
u
n
d
e
r
s
tan
d
in
g
s
tag
e,
th
e
s
y
s
tem
m
ay
p
r
o
v
id
e
s
ca
f
f
o
ld
in
g
th
at
f
o
c
u
s
es
o
n
v
is
u
al
r
ep
r
esen
tatio
n
o
r
p
r
o
b
lem
d
ec
o
m
p
o
s
itio
n
.
I
n
co
n
tr
ast,
wh
en
d
if
f
icu
lties
ar
is
e
at
th
e
s
tag
e
o
f
ex
ec
u
tin
g
th
e
p
lan
,
s
ca
f
f
o
l
d
in
g
ca
n
b
e
in
th
e
f
o
r
m
o
f
s
tep
-
by
-
s
tep
g
u
id
an
ce
o
r
r
e
m
in
d
er
s
ab
o
u
t k
ey
co
n
ce
p
ts
[
9
]
,
[
1
0
]
.
T
h
is
ap
p
r
o
ac
h
h
elp
s
ad
d
r
es
s
s
p
ec
if
ic
d
if
f
icu
lties
in
g
eo
m
etr
y
p
r
o
b
lem
s
o
lv
in
g
an
d
p
r
o
m
o
tes
s
tu
d
en
ts
’
awa
r
en
ess
o
f
co
g
n
itiv
e
p
r
o
ce
s
s
es
d
u
r
in
g
p
r
o
b
lem
s
o
lv
in
g
.
Stu
d
en
ts
b
ec
o
m
e
m
o
r
e
co
n
s
cio
u
s
o
f
th
e
s
tr
ateg
ies
an
d
er
r
o
r
s
b
y
p
r
o
m
o
tin
g
r
ef
lectio
n
at
ea
ch
s
tep
o
f
Pó
ly
a’
s
p
r
o
b
lem
-
s
o
lv
in
g
f
r
am
ewo
r
k
[
5
]
,
[
2
1
]
.
T
h
er
ef
o
r
e,
th
e
lear
n
in
g
p
r
o
ce
s
s
f
o
cu
s
es
o
n
o
b
tain
i
n
g
co
r
r
e
ct
an
s
wer
s
an
d
em
p
h
asizes
th
e
d
e
v
elo
p
m
e
n
t
o
f
tr
an
s
f
er
ab
le
m
etac
o
g
n
itiv
e
s
k
i
lls
.
T
h
e
d
e
v
elo
p
m
e
n
t
o
f
FIS
-
b
a
s
ed
s
ca
f
f
o
ld
in
g
s
y
s
tem
s
f
o
r
g
eo
m
etr
y
lear
n
in
g
o
f
f
e
r
s
a
p
r
o
m
is
in
g
o
p
p
o
r
tu
n
ity
t
o
ad
d
r
ess
lo
n
g
-
s
tan
d
in
g
c
h
allen
g
es
in
t
h
is
f
ield
.
T
h
e
s
y
s
tem
s
ca
n
en
h
an
ce
th
e
lear
n
in
g
ex
p
er
ien
ce
an
d
im
p
r
o
v
e
s
tu
d
e
n
t
o
u
tc
o
m
es
b
y
in
c
o
r
p
o
r
atin
g
a
th
o
r
o
u
g
h
u
n
d
er
s
tan
d
i
n
g
o
f
s
tu
d
en
t
c
h
allen
g
es,
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
2
5
2
-
8
9
3
8
I
n
t J Ar
tif
I
n
tell
,
Vo
l.
15
,
No
.
4
,
Au
g
u
s
t 2
0
2
6
:
3
2
8
6
-
3
2
9
8
3288
th
e
p
r
in
cip
les
o
f
ef
f
ec
ti
v
e
s
ca
f
f
o
ld
in
g
,
an
d
th
e
ad
a
p
tiv
e
ca
p
a
b
ilit
ies
o
f
FIS.
Ho
wev
er
,
th
e
r
ea
lizatio
n
r
eq
u
ir
es
s
tr
o
n
g
in
ter
d
is
cip
lin
ar
y
co
lla
b
o
r
atio
n
b
etwe
en
m
ath
e
m
atics
teac
h
er
s
,
g
eo
m
etr
y
d
o
m
ain
ex
p
er
ts
,
lear
n
in
g
s
y
s
tem
d
esig
n
er
s
,
an
d
ed
u
ca
tio
n
al
ex
p
er
ts
.
L
ea
r
n
in
g
to
o
ls
a
d
d
r
ess
in
g
d
if
f
icu
lties
in
g
e
o
m
etr
y
an
d
en
h
an
cin
g
d
ee
p
er
ap
p
r
ec
iatio
n
o
f
m
at
h
e
m
atics a
m
o
n
g
s
tu
d
en
ts
ar
e
d
ev
elo
p
ed
th
r
o
u
g
h
th
is
co
llab
o
r
ativ
e
ef
f
o
r
t.
2.
M
E
T
H
O
D
FIS
was
cr
ea
ted
b
y
ad
ap
tin
g
th
e
r
ap
id
ap
p
licatio
n
d
ev
elo
p
m
en
t
(
R
AD)
m
eth
o
d
o
lo
g
y
,
wh
ich
in
clu
d
es
f
o
u
r
s
tag
es:
p
r
o
to
ty
p
e
d
esig
n
,
r
eq
u
ir
e
m
en
ts
p
lan
n
i
n
g
,
a
n
d
iter
ativ
e
co
n
s
tr
u
ctio
n
[
3
3
]
.
Acc
o
r
d
i
n
g
to
Po
u
r
jav
ad
a
n
d
Ma
y
o
r
g
a
[
3
4
]
,
th
e
f
u
zz
y
Ma
m
d
an
i
m
et
h
o
d
f
o
r
ca
lcu
latin
g
co
n
tr
o
l
o
u
tp
u
t
s
co
n
s
is
ts
o
f
th
r
ee
p
r
im
ar
y
s
tep
s
.
T
h
ese
s
tep
s
ar
e
ev
alu
atio
n
,
f
u
zz
if
icatio
n
,
a
n
d
d
ef
u
zz
if
icatio
n
.
2
.
1
.
P
l
a
nn
ing
p
ha
s
e
T
h
e
p
lan
n
in
g
p
h
ase
s
tar
ts
wit
h
th
e
in
itial
s
tag
e
o
f
th
e
Ma
m
d
an
i
m
eth
o
d
,
ca
lled
f
u
zz
if
icatio
n
,
wh
er
e
in
p
u
t
an
d
o
u
t
p
u
t
v
a
r
iab
les
ar
e
id
en
tifie
d
an
d
th
eir
r
esp
ec
tiv
e
f
u
zz
y
s
ets
ar
e
d
e
f
in
ed
.
I
n
t
h
e
Ma
m
d
an
i
m
eth
o
d
,
b
o
th
i
n
p
u
t
an
d
o
u
tp
u
t
v
ar
ia
b
les
ar
e
s
eg
m
e
n
ted
i
n
to
o
n
e
o
r
m
o
r
e
f
u
zz
y
s
ets.
Seco
n
d
ly
,
r
u
le
e
v
alu
atio
n
in
co
r
p
o
r
ates
th
e
im
p
licatio
n
f
u
n
ctio
n
th
r
o
u
g
h
m
in
a
n
d
r
u
le
co
m
p
o
s
itio
n
.
Du
r
in
g
th
is
s
tag
e,
th
e
im
p
licatio
n
f
u
n
ctio
n
e
m
p
lo
y
e
d
is
m
in
,
a
n
d
th
e
r
u
le
co
m
p
o
s
itio
n
r
esu
lts
f
r
o
m
t
h
e
in
f
er
e
n
ce
p
r
o
ce
s
s
.
T
h
e
m
ax
m
eth
o
d
is
u
s
ed
am
o
n
g
t
h
e
th
r
ee
in
f
e
r
en
ce
m
eth
o
d
s
av
ailab
le.
T
h
e
d
e
f
u
zz
if
icatio
n
s
tag
e
em
p
lo
y
s
th
e
ce
n
tr
o
id
o
f
ar
ea
(
C
OA
)
m
et
h
o
d
f
o
r
d
e
f
u
zz
if
ica
t
io
n
wit
h
i
n
Ma
m
d
a
n
i'
s
f
u
zz
y
r
u
le
co
m
p
o
s
iti
o
n
.
T
h
is
p
r
o
ce
s
s
is
ill
u
s
t
r
a
te
d
b
y
(
1
)
.
z
=
∑
μ
D
∑
μ
(
1
)
W
h
er
e
μ
r
ep
r
esen
ts
th
e
m
e
m
b
er
s
h
ip
d
eg
r
ee
o
f
t
h
e
f
u
zz
y
s
et
an
d
D
d
en
o
tes a
p
r
ec
is
e
n
u
m
b
er
.
FIS
ad
o
p
ts
m
u
lti
-
in
p
u
t
s
in
g
le
-
o
u
tp
u
t
(
MI
SO)
s
tr
u
ctu
r
e,
in
wh
ich
th
e
in
p
u
ts
co
n
s
is
t
o
f
s
ca
f
f
o
ld
in
g
co
m
p
o
n
en
ts
r
eq
u
ir
ed
to
ad
d
r
ess
er
r
o
r
s
in
s
o
lv
in
g
g
eo
m
etr
y
p
r
o
b
lem
s
,
wh
ile
th
e
o
u
tp
u
t
r
e
p
r
esen
ts
th
e
ap
p
r
o
p
r
iate
lev
el.
T
h
is
s
tu
d
y
r
ef
er
s
to
Pó
ly
a'
s
s
tag
es
o
f
p
r
o
b
lem
s
o
lv
i
n
g
,
wh
ich
in
clu
d
e
u
n
d
er
s
tan
d
in
g
th
e
p
r
o
b
lem
,
as
well
as
p
lan
n
in
g
,
im
p
lem
en
tin
g
,
an
d
r
e
-
e
x
am
in
i
n
g
th
e
s
o
lu
tio
n
.
T
h
is
s
tu
d
y
cla
s
s
if
ies
s
ca
f
f
o
ld
in
g
co
m
p
o
n
en
ts
in
to
th
r
e
e
ca
teg
o
r
ies
ad
ju
s
ted
to
Pó
ly
a'
s
s
tag
es
,
n
am
ely
e
n
v
ir
o
n
m
en
tal
p
r
o
v
i
s
io
n
s
,
ex
p
lan
atio
n
,
r
ev
iew,
r
estru
ctu
r
in
g
,
an
d
d
e
v
elo
p
in
g
co
n
ce
p
tu
al
th
in
k
i
n
g
,
b
y
r
ef
er
r
i
n
g
to
th
e
[
3
5
]
s
ca
f
f
o
ld
in
g
m
o
d
el.
E
ac
h
co
m
p
o
n
en
t
is
r
ated
with
a
ce
r
tain
s
ca
le,
an
d
th
e
f
u
zz
y
s
y
s
tem
p
r
o
d
u
ce
s
o
u
tp
u
t
in
th
e
f
o
r
m
o
f
s
ca
f
f
o
ld
in
g
lev
els
d
iv
id
ed
in
to
in
itial,
ad
v
an
ce
d
,
in
d
ep
en
d
en
t,
an
d
h
ig
h
in
d
ep
en
d
en
ce
.
T
h
is
s
tu
d
y
a
im
s
to
p
er
s
o
n
alize
lear
n
in
g
s
u
p
p
o
r
t
b
ased
o
n
s
tu
d
en
ts
'
er
r
o
r
s
in
s
o
lv
in
g
g
e
o
m
etr
y
p
r
o
b
lem
s
to
im
p
r
o
v
e
u
n
d
er
s
tan
d
i
n
g
a
n
d
in
d
ep
en
d
en
ce
.
A
n
g
h
iler
i’
s
[
3
5
]
s
ca
f
f
o
l
d
in
g
f
r
am
ewo
r
k
is
m
ap
p
ed
o
n
to
ea
ch
s
tag
e
o
f
p
r
o
b
lem
s
o
lv
in
g
to
clar
if
y
th
e
r
elatio
n
s
h
ip
b
etwe
en
s
ca
f
f
o
ld
in
g
co
m
p
o
n
en
ts
a
n
d
Pó
ly
a’
s
p
r
o
b
lem
-
s
o
lv
in
g
s
tag
es.
T
h
e
m
ap
p
in
g
r
ep
o
r
ts
h
o
w
d
if
f
er
en
t
s
ca
f
f
o
ld
in
g
s
tr
ateg
ies
s
u
p
p
o
r
t
s
tu
d
en
t
s
at
s
p
ec
if
ic
co
g
n
itiv
e
s
tag
es.
T
ab
le
1
p
r
o
v
id
es
a
d
etailed
d
escr
ip
tio
n
o
f
th
e
s
ca
f
f
o
ld
in
g
c
o
m
p
o
n
en
ts
.
T
ab
le
1
.
Descr
ip
tio
n
o
f
s
ca
f
f
o
ld
in
g
co
m
p
o
n
en
ts
ass
o
ciate
d
with
Pó
ly
a'
s
p
r
o
b
lem
-
s
o
lv
in
g
s
t
ag
es
A
n
g
h
i
l
e
r
i
'
s sc
a
f
f
o
l
d
i
n
g
c
o
m
p
o
n
e
n
t
S
t
a
g
e
s
o
f
p
r
o
b
l
e
m s
o
l
v
i
n
g
P
o
l
y
a
En
v
i
r
o
n
m
e
n
t
a
l
p
r
o
v
i
s
i
o
n
s
(
e
p
)
U
n
d
e
r
st
a
n
d
t
h
e
p
r
o
b
l
e
m
:
‒
V
i
su
a
l
i
z
e
t
h
e
p
r
o
b
l
e
m
‒
R
e
o
r
g
a
n
i
z
e
f
a
c
t
s
a
n
d
p
r
o
b
l
e
ms
u
s
i
n
g
o
w
n
l
a
n
g
u
a
g
e
Ex
p
l
a
i
n
i
n
g
,
r
e
v
i
e
w
i
n
g
,
a
n
d
r
e
st
r
u
c
t
u
r
i
n
g
(
e
r
)
M
a
k
e
a
p
l
a
n
:
‒
M
a
k
e
c
o
n
n
e
c
t
i
o
n
s fr
o
m w
h
a
t
i
s
k
n
o
w
n
(
f
a
c
t
s)
t
o
t
h
e
p
r
o
b
l
e
m
‒
D
e
v
e
l
o
p
a
p
r
o
b
l
e
m
-
s
o
l
v
i
n
g
p
l
a
n
o
r
s
t
r
a
t
e
g
y
b
a
se
d
o
n
c
o
n
c
e
p
t
s re
l
a
t
e
d
t
o
t
h
e
p
r
o
b
l
e
m
C
a
r
r
y
o
u
t
t
h
e
p
l
a
n
:
‒
A
p
p
l
y
t
h
e
c
o
n
c
e
p
t
s
a
n
d
st
r
a
t
e
g
i
e
s
t
h
a
t
h
a
v
e
b
e
e
n
c
h
o
se
n
t
o
s
o
l
v
e
t
h
e
p
r
o
b
l
e
m.
‒
P
e
r
f
o
r
m c
a
l
c
u
l
a
t
i
o
n
s
c
a
r
e
f
u
l
l
y
a
n
d
t
h
o
r
o
u
g
h
l
y
.
D
e
v
e
l
o
p
i
n
g
c
o
n
c
e
p
t
u
a
l
t
h
i
n
k
i
n
g
(
d
c
)
Lo
o
k
b
a
c
k
:
‒
A
n
sw
e
r
p
r
o
b
l
e
ms
b
a
s
e
d
o
n
p
r
o
b
l
e
m
-
s
o
l
v
i
n
g
a
n
d
r
e
f
l
e
c
t
o
n
t
h
e
a
n
sw
e
r
s
t
h
a
t
h
a
v
e
b
e
e
n
mad
e
.
‒
Lo
o
k
f
o
r
o
t
h
e
r
a
l
t
e
r
n
a
t
i
v
e
s
t
o
s
o
l
v
e
t
h
e
p
r
o
b
l
e
m
o
r
t
h
e
p
o
ssi
b
i
l
i
t
y
o
f
o
t
h
e
r
c
o
n
c
e
p
t
s
r
e
l
a
t
e
d
t
o
t
h
e
p
r
o
b
l
e
m
a
t
h
a
n
d
.
2
.
2
.
P
r
o
t
o
t
y
pe
d
esig
n
Du
r
in
g
th
e
p
r
o
to
ty
p
e
d
esig
n
p
h
ase,
ea
ch
cr
iter
io
n
was
ev
alu
ated
an
d
class
if
ied
in
to
th
r
ee
ca
teg
o
r
ies:
s
tr
o
n
g
,
m
o
d
er
ate,
a
n
d
wea
k
,
ea
ch
with
its
o
wn
v
alu
e
r
an
g
e.
T
h
e
d
o
m
ain
in
ter
v
al
o
f
ea
ch
in
p
u
t
v
ar
iab
le
is
ad
ju
s
ted
to
th
e
n
u
m
b
er
o
f
d
escr
ip
to
r
s
f
r
o
m
th
e
v
ar
iab
le.
A
d
escr
ip
to
r
was
ass
ess
ed
at
a
m
ax
im
u
m
o
f
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Ar
tif
I
n
tell
I
SS
N:
2252
-
8
9
3
8
Dete
r
min
in
g
s
tu
d
en
t sca
ffo
ld
in
g
leve
ls
in
g
eo
metry
p
r
o
b
lem
-
s
o
lvin
g
:
a
f
u
z
z
y
…
(
Yu
n
ia
r
I
k
a
P
u
tr
i P
r
a
n
ya
ta
)
3289
1
0
p
o
in
ts
.
T
h
e
en
v
ir
o
n
m
e
n
tal
p
r
o
v
is
io
n
s
v
ar
iab
le
h
as
2
d
escr
ip
to
r
s
s
in
ce
th
e
d
o
m
ain
in
ter
v
al
is
[
0
,
2
0
]
.
T
h
e
ex
p
lain
in
g
,
r
ev
iewin
g
,
a
n
d
r
e
s
tr
u
ctu
r
in
g
v
a
r
iab
le
h
as
4
d
es
cr
ip
to
r
s
,
an
d
t
h
e
d
o
m
ai
n
in
te
r
v
al
is
[
0
,
4
0
]
.
T
h
e
d
ev
el
o
p
in
g
c
o
n
ce
p
tu
al
th
in
k
in
g
v
ar
ia
b
le
h
as
2
d
escr
ip
to
r
s
,
a
n
d
th
e
d
o
m
ain
in
ter
v
al
is
[
0
,
2
0
]
.
T
a
b
le
2
d
is
p
lay
s
th
e
r
an
g
e
o
f
v
alu
es f
o
r
t
h
e
th
r
e
e
cr
iter
ia.
T
h
e
r
a
n
g
e
s
er
v
es a
s
d
ata
to
ass
ess
th
e
d
eg
r
ee
o
f
s
tu
d
en
t scaf
f
o
ld
in
g
.
2
.
3
.
I
t
er
a
t
iv
e
c
o
ns
t
ruct
io
n
Du
r
in
g
t
h
e
p
r
o
to
ty
p
e
d
e
v
elo
p
m
en
t
s
tag
e,
th
e
m
ai
n
co
m
p
o
n
en
t
d
is
p
lay
o
f
th
e
Ma
m
d
a
n
i
FIS
was
d
esig
n
ed
b
y
f
o
c
u
s
in
g
o
n
f
o
u
r
f
u
n
ctio
n
al
m
o
d
u
les
,
as
s
h
o
wn
in
Fig
u
r
e
1
.
T
h
e
o
v
er
all
s
tr
u
ct
u
r
e
o
f
th
e
p
r
o
p
o
s
ed
Ma
m
d
an
i
FIS
is
illu
s
tr
ated
in
Fig
u
r
e
2
.
T
h
e
ar
c
h
itectu
r
e
p
r
o
g
r
ess
es
f
r
o
m
lef
t
to
r
ig
h
t,
tr
an
s
itio
n
in
g
f
r
o
m
th
r
ee
in
p
u
ts
(
ep
,
e
r
,
an
d
d
c)
to
th
e
o
u
tp
u
t (
s
ca
f
f
o
ld
in
g
le
v
el)
.
Fig
u
r
e
1
.
Diag
r
a
m
o
f
Ma
m
d
an
i FI
S m
o
d
el
u
s
ed
in
th
is
s
tu
d
y
Fig
u
r
e
2
.
Diag
r
a
m
th
e
in
p
u
ts
a
n
d
o
u
t
p
u
ts
o
f
th
e
p
r
o
p
o
s
ed
Ma
m
d
an
i FI
S m
o
d
el
u
s
ed
to
id
e
n
tify
s
tu
d
en
ts
’
s
ca
f
f
o
ld
in
g
lev
els
3.
RE
SU
L
T
S AN
D
D
I
SCU
SS
I
O
N
T
h
e
f
u
zz
y
s
y
s
tem
was
cr
ea
te
d
u
s
in
g
t
h
e
Ma
m
d
a
n
i
m
eth
o
d
b
y
co
m
b
in
in
g
th
e
p
r
im
ar
y
f
u
n
ctio
n
al
m
o
d
u
les,
n
am
el
y
f
u
zz
if
icatio
n
,
in
f
er
e
n
ce
,
r
u
le
ev
alu
atio
n
,
an
d
d
ef
u
zz
if
icatio
n
.
E
ac
h
m
o
d
u
le
p
lay
s
a
cr
u
cial
r
o
le
in
p
r
o
ce
s
s
in
g
s
tu
d
en
t
p
e
r
f
o
r
m
a
n
ce
d
ata
an
d
c
o
n
v
e
r
tin
g
th
e
co
n
te
x
t
in
to
m
ea
n
i
n
g
f
u
l
s
ca
f
f
o
ld
in
g
-
lev
el
r
ec
o
m
m
en
d
atio
n
s
.
T
h
is
s
tr
u
ctu
r
ed
ap
p
r
o
ac
h
allo
ws
th
e
s
y
s
tem
to
m
an
ag
e
u
n
ce
r
tain
ties
in
s
tu
d
en
t
er
r
o
r
s
an
d
o
f
f
er
a
d
ap
tiv
e
s
u
p
p
o
r
t a
lig
n
ed
with
in
s
tr
u
ctio
n
al
r
eq
u
i
r
em
en
t
s
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
2
5
2
-
8
9
3
8
I
n
t J Ar
tif
I
n
tell
,
Vo
l.
15
,
No
.
4
,
Au
g
u
s
t 2
0
2
6
:
3
2
8
6
-
3
2
9
8
3290
3
.
1
.
F
uzzif
ica
t
io
n
Fu
zz
y
l
o
g
ic
is
u
tili
ze
d
to
a
n
aly
ze
r
ea
l
-
tim
e
ex
p
er
im
en
ta
l
in
p
u
ts
an
d
ass
ess
th
eir
m
em
b
er
s
h
ip
lev
els
[
3
6
]
.
Fu
zz
if
icatio
n
is
a
co
m
p
o
n
en
t
o
f
f
u
zz
y
lo
g
ic
th
at
tr
an
s
f
o
r
m
s
cr
is
p
d
ata
in
to
f
u
zz
y
v
alu
es
r
an
g
in
g
f
r
o
m
0
to
1
[
3
7
]
.
I
n
th
is
co
n
te
x
t,
a
v
alu
e
o
f
1
in
d
icate
s
f
u
ll (
1
0
0
%)
m
em
b
e
r
s
h
ip
in
th
e
f
u
z
zy
s
et,
wh
ile
a
v
alu
e
of
0
in
d
icate
s
n
o
(
0
%)
m
em
b
e
r
s
h
ip
.
T
ab
le
2
p
r
esen
ts
d
etails
o
n
lin
g
u
is
tic
v
a
r
iab
les
lin
k
ed
to
ea
ch
p
ar
am
eter
,
f
ac
ilit
atin
g
a
th
o
r
o
u
g
h
u
n
d
er
s
tan
d
in
g
o
f
t
h
e
f
u
zz
y
s
ets.
Fu
zz
y
in
p
u
ts
s
h
o
u
ld
b
e
u
tili
ze
d
with
Ma
m
d
an
i
FIS.
T
o
tr
an
s
f
o
r
m
cr
is
p
in
p
u
ts
in
to
f
u
zz
y
o
n
es,
m
em
b
er
s
h
ip
f
u
n
ctio
n
s
ar
e
em
p
lo
y
ed
to
d
ef
in
e
in
p
u
t
s
ets.
T
ab
le
2
illu
s
tr
ates
v
ar
io
u
s
f
o
r
m
s
o
f
m
em
b
e
r
s
h
ip
f
u
n
ctio
n
s
t
h
at
r
ep
r
esen
t
d
i
f
f
er
en
t
le
v
els
o
f
f
u
zz
i
n
ess
ac
r
o
s
s
v
ar
io
u
s
s
ce
n
ar
io
s
.
T
ab
le
2
.
Fu
zz
y
lin
g
u
is
tic
v
ar
ia
b
les f
o
r
ea
ch
p
ar
am
eter
P
a
r
a
me
t
e
r
C
o
d
e
Li
n
g
u
i
s
t
i
c
v
a
r
i
a
b
l
e
R
a
n
g
e
R
e
p
r
e
se
n
t
a
t
i
o
n
I
n
p
u
t
(
3
)
ep
S
t
r
o
n
g
(
T)
1
2
–
20
F
i
g
u
r
e
3
M
o
d
e
r
a
t
e
(
S
)
0
4
–
16
W
e
a
k
(
R
)
0
0
–
08
er
S
t
r
o
n
g
(
T)
2
4
–
40
F
i
g
u
r
e
4
M
o
d
e
r
a
t
e
(
S
)
0
8
–
32
W
e
a
k
(
R
)
0
0
–
16
dc
S
t
r
o
n
g
(
T)
1
2
–
20
F
i
g
u
r
e
5
M
o
d
e
r
a
t
e
(
S
)
0
4
–
16
W
e
a
k
(
R
)
0
0
–
08
O
u
t
p
u
t
Le
v
e
l
B
e
g
i
n
n
e
r
l
e
v
e
l
(
LA
)
0
0
–
30
F
i
g
u
r
e
6
A
d
v
a
n
c
e
d
l
e
v
e
l
(
LL)
1
0
–
50
I
n
d
e
p
e
n
d
e
n
t
l
e
v
e
l
(
LI
)
3
0
–
70
H
i
g
h
i
n
d
e
p
e
n
d
e
n
c
e
(
L
K
T)
5
0
–
80
3
.
1
.
1
.
I
np
ut
v
a
ria
ble
env
iro
nm
ent
a
l pro
v
is
io
ns
:
dev
elo
pin
g
co
ncept
ua
l t
hin
k
ing
T
h
e
r
an
g
e
f
o
r
ea
ch
ca
teg
o
r
y
is
ca
lcu
lated
b
ased
o
n
th
e
an
aly
s
is
o
f
s
tu
d
en
t
test
r
esu
lt
s
wh
e
n
wo
r
k
in
g
o
n
g
e
o
m
etr
y
p
r
o
b
lem
s
an
d
a
d
j
u
s
ted
ac
co
r
d
in
g
to
T
ab
le
1
.
Fig
u
r
es
3
to
6
d
is
p
lay
f
u
zz
y
m
e
m
b
er
s
h
ip
f
u
n
ctio
n
s
cr
ea
ted
with
Mic
r
o
s
o
f
t
E
x
ce
l.
T
h
e
f
o
u
r
f
ig
u
r
es
illu
s
tr
ate
a
m
em
b
er
s
h
ip
f
u
n
ctio
n
co
m
p
o
s
ed
o
f
a
co
m
b
in
atio
n
o
f
tr
ap
ez
o
i
d
al
s
h
ap
es.
T
h
is
is
co
m
m
o
n
l
y
u
s
ed
b
ec
a
u
s
e
o
f
its
s
im
p
licity
an
d
ca
n
b
e
r
ep
r
ese
n
ted
u
s
in
g
a
s
tr
aig
h
t
lin
e
[
3
8
]
.
T
o
en
h
an
ce
r
e
p
r
o
d
u
cib
ilit
y
,
th
e
ex
ac
t
p
ar
am
eter
s
ettin
g
s
o
f
th
e
tr
ap
ez
o
id
al
m
e
m
b
er
s
h
ip
f
u
n
ctio
n
s
ar
e
ex
p
licitly
p
r
o
v
i
d
ed
in
T
a
b
le
3
.
T
h
ese
p
ar
am
eter
s
d
ef
i
n
e
th
e
lo
wer
,
u
p
p
er
,
an
d
o
v
e
r
lap
p
in
g
r
eg
io
n
s
f
o
r
ea
ch
f
u
zz
y
s
et.
T
ab
le
3
.
Par
am
eter
s
o
f
th
e
tr
a
p
ez
o
id
al
m
em
b
er
s
h
ip
f
u
n
ctio
n
V
a
r
i
a
b
l
e
F
u
z
z
y
s
et
a
b
c
d
ep
W
e
a
k
0
0
4
8
ep
M
o
d
e
r
a
t
e
4
8
12
16
ep
S
t
r
o
n
g
12
16
20
20
er
W
e
a
k
0
0
8
16
er
M
o
d
e
r
a
t
e
8
16
24
32
er
S
t
r
o
n
g
24
32
40
40
dc
W
e
a
k
0
0
4
8
dc
M
o
d
e
r
a
t
e
4
8
12
16
dc
S
t
r
o
n
g
12
16
20
20
Fig
u
r
e
3
.
Mo
d
el
p
er
f
o
r
m
a
n
ce
u
s
in
g
a
tr
ap
ez
o
id
al
m
em
b
e
r
s
h
ip
f
u
n
ctio
n
f
o
r
ep
i
n
p
u
t
v
ar
iab
l
e
0
0
.
2
0
.
4
0
.
6
0
.
8
1
1
.
2
0
4
8
12
16
20
M
e
mb
e
r
sh
i
p
d
e
g
r
e
e
S
c
a
f
f
o
l
d
i
n
g
sco
r
e
o
f
e
n
v
i
r
o
n
me
n
t
a
l
p
r
o
v
i
si
o
n
s
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Ar
tif
I
n
tell
I
SS
N:
2252
-
8
9
3
8
Dete
r
min
in
g
s
tu
d
en
t sca
ffo
ld
in
g
leve
ls
in
g
eo
metry
p
r
o
b
lem
-
s
o
lvin
g
:
a
f
u
z
z
y
…
(
Yu
n
ia
r
I
k
a
P
u
tr
i P
r
a
n
ya
ta
)
3291
Fig
u
r
e
4
.
Mo
d
el
p
er
f
o
r
m
a
n
ce
u
s
in
g
a
tr
ap
ez
o
id
al
m
em
b
e
r
s
h
ip
f
u
n
ctio
n
f
o
r
er
i
n
p
u
t
v
ar
iab
l
e
Fig
u
r
e
5
.
Mo
d
el
p
er
f
o
r
m
a
n
ce
u
s
in
g
a
tr
ap
ez
o
id
al
m
em
b
e
r
s
h
ip
f
u
n
ctio
n
f
o
r
d
c
i
n
p
u
t
v
ar
iab
l
e
Fig
u
r
e
6
.
T
h
e
m
em
b
er
s
h
ip
f
u
n
ctio
n
s
f
o
r
th
e
o
u
tp
u
t
v
ar
iab
le
t
o
r
ep
r
esen
tin
g
s
ca
f
f
o
ld
i
n
g
lev
els p
r
o
d
u
ce
d
Fig
u
r
es
3
to
5
illu
s
tr
ate
th
e
u
s
e
o
f
th
e
i
n
f
er
en
ce
s
y
s
tem
to
g
en
er
ate
th
e
in
p
u
t
f
o
r
th
e
f
u
zz
y
d
ec
is
io
n
in
d
e
x
.
T
h
e
eq
u
atio
n
u
s
ed
to
d
eter
m
in
e
th
e
f
u
zz
y
m
em
b
er
s
h
ip
v
alu
e
o
f
t
h
e
en
v
ir
o
n
m
e
n
tal
p
r
o
v
is
io
n
s
(
ep
)
in
p
u
t
s
et
is
d
iv
id
ed
in
to
th
r
ee
f
u
zz
y
s
ets:
wea
k
(
ep
R
)
,
m
o
d
er
ate
(
e
p
S),
an
d
s
tr
o
n
g
(
ep
T
)
,
as
s
h
o
wn
in
(
2
)
to
(
4
)
.
T
h
e
v
alu
e
o
f
x
is
th
e
test
r
esu
lts
o
f
g
eo
m
etr
y
q
u
e
s
tio
n
s
ad
ju
s
ted
to
T
ab
le
4
.
B
ef
o
r
e
p
r
esen
tin
g
th
e
m
ath
em
atica
l
eq
u
atio
n
s
o
f
t
h
e
m
em
b
e
r
s
h
ip
f
u
n
ctio
n
s
,
th
e
r
elatio
n
s
h
ip
b
etwe
en
in
p
u
t
v
ar
iab
les
an
d
th
e
0
0
.
2
0
.
4
0
.6
0
.
8
1
1
.
2
0
8
16
24
32
40
M
e
mb
e
r
sh
i
p
d
e
g
r
e
e
S
c
a
f
f
o
l
d
i
n
g
sco
r
e
o
f
e
x
p
l
a
i
n
i
n
g
,
r
e
v
i
e
w
i
n
g
,
a
n
d
r
e
st
r
u
c
t
u
r
e
d
0
0
.
2
0
.
4
0
.
6
0
.
8
1
1
.
2
0
4
8
12
16
20
M
e
mb
e
r
sh
i
p
d
e
g
r
e
e
S
c
a
f
f
o
l
d
i
n
g
sco
r
e
o
f
d
e
v
e
l
o
p
i
n
g
c
o
n
c
e
p
t
u
a
l
t
h
i
n
k
i
n
g
0
0
.
2
0
.
4
0
.
6
0
.
8
1
1
.
2
0
10
20
30
40
50
60
70
80
M
e
mb
e
r
sh
i
p
d
e
g
r
e
e
R
a
t
e
o
f
st
u
d
e
n
t
sca
f
f
o
l
d
i
n
g
l
e
v
e
l
s
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
2
5
2
-
8
9
3
8
I
n
t J Ar
tif
I
n
tell
,
Vo
l.
15
,
No
.
4
,
Au
g
u
s
t 2
0
2
6
:
3
2
8
6
-
3
2
9
8
3292
co
r
r
esp
o
n
d
in
g
f
u
zz
y
s
ets
is
s
u
m
m
ar
ized
to
im
p
r
o
v
e
clar
ity
an
d
r
ea
d
ab
ilit
y
.
T
h
is
s
u
m
m
ar
y
allo
ws
s
tu
d
en
ts
to
u
n
d
er
s
tan
d
t
h
e
s
tr
u
ctu
r
e
o
f
th
e
f
u
zz
y
m
o
d
el
b
e
f
o
r
e
t
h
e
f
o
r
m
a
l f
o
r
m
u
latio
n
.
(
)
=
{
1
,
<
4
8
−
4
,
4
≤
<
8
0
,
≥
8
(
2
)
(
)
=
{
0
,
<
4
−
4
4
,
4
≤
<
8
1
,
8
≤
<
12
16
−
4
,
12
≤
<
16
0
,
≥
16
(
3
)
(
)
=
{
0
,
<
12
−
12
4
,
12
≤
<
16
1
,
≥
16
(
4
)
T
h
e
eq
u
atio
n
u
s
ed
to
ca
lcu
lat
e
th
e
f
u
zz
y
m
em
b
er
s
h
ip
v
alu
e
o
f
t
h
e
in
p
u
t
s
et
f
o
r
e
x
p
lain
i
n
g
,
r
ev
iewin
g
,
an
d
r
estru
c
tu
r
ed
(
er
)
is
d
iv
i
d
ed
in
t
o
th
r
ee
f
u
zz
y
s
ets:
wea
k
(
er
R
)
,
m
o
d
er
ate
(
er
S),
an
d
s
tr
o
n
g
(
er
T
)
,
as
s
h
o
wn
in
(
5
)
to
(
7
)
.
T
h
e
v
al
u
e
o
f
x
is
th
e
test
r
esu
lts
o
f
g
eo
m
etr
y
q
u
es
tio
n
s
ad
ju
s
ted
to
T
ab
le
4
.
(
)
=
{
1
,
<
8
16
−
8
,
8
≤
<
16
0
,
≥
16
(
5
)
(
)
=
{
0
,
<
8
−
8
8
,
8
≤
<
16
1
,
16
≤
<
24
32
−
8
,
24
≤
<
32
0
,
≥
32
(
6
)
(
)
=
{
0
,
<
24
−
24
8
,
24
≤
<
32
1
,
≥
32
(
7
)
T
h
e
eq
u
atio
n
to
d
eter
m
i
n
e
th
e
f
u
zz
y
m
em
b
e
r
s
h
ip
v
alu
e
f
o
r
d
ev
elo
p
in
g
co
n
ce
p
tu
al
th
in
k
in
g
(
d
c
)
is
s
p
lit
in
t
o
wea
k
(
d
cR),
m
o
d
e
r
ate
(
d
cS)
,
a
n
d
s
tr
o
n
g
(
d
cT
)
f
u
zz
y
v
alu
es,
as
s
h
o
wn
in
(
8
)
to
(
1
0
)
.
T
h
e
v
alu
e
o
f
x
is
th
e
test
r
esu
lts
o
f
g
eo
m
etr
y
q
u
esti
o
n
s
ad
ju
s
ted
to
T
ab
le
4
.
(
)
=
{
1
,
<
4
8
−
4
,
4
≤
<
8
0
,
≥
8
(
8
)
(
)
=
{
0
,
<
4
−
4
4
,
4
≤
<
8
1
,
8
≤
<
12
16
−
4
,
12
≤
<
16
0
,
≥
16
(
9
)
(
)
=
{
0
,
<
12
−
12
4
,
12
≤
<
16
1
,
≥
16
(
1
0
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Ar
tif
I
n
tell
I
SS
N:
2252
-
8
9
3
8
Dete
r
min
in
g
s
tu
d
en
t sca
ffo
ld
in
g
leve
ls
in
g
eo
metry
p
r
o
b
lem
-
s
o
lvin
g
:
a
f
u
z
z
y
…
(
Yu
n
ia
r
I
k
a
P
u
tr
i P
r
a
n
ya
ta
)
3293
T
ab
le
4
.
De
f
in
itio
n
o
f
t
h
e
m
e
m
b
er
s
h
ip
d
e
g
r
ee
f
o
r
th
e
i
n
p
u
t
v
ar
iab
le
r
elate
d
to
s
ca
f
f
o
ld
in
g
co
m
p
o
n
en
ts
I
n
p
u
t
v
a
r
i
a
b
l
e
C
o
d
e
F
u
z
z
y
s
e
t
s
D
o
ma
i
n
En
v
i
r
o
n
m
e
n
t
a
l
p
r
o
v
i
s
i
o
n
s
ep
W
e
a
k
,
m
o
d
e
r
a
t
e
,
st
r
o
n
g
[0
–
20]
Ex
p
l
a
i
n
i
n
g
,
r
e
v
i
e
w
i
n
g
,
r
e
s
t
r
u
c
t
u
r
i
n
g
er
W
e
a
k
,
m
o
d
e
r
a
t
e
,
st
r
o
n
g
[0
–
40]
D
e
v
e
l
o
p
i
n
g
c
o
n
c
e
p
t
u
a
l
t
h
i
n
k
i
n
g
dc
W
e
a
k
,
m
o
d
e
r
a
t
e
,
st
r
o
n
g
[0
–
20]
O
u
t
p
u
t
l
e
v
e
l
B
e
g
i
n
n
e
r
,
a
d
v
a
n
c
e
d
,
i
n
d
e
p
e
n
d
e
n
t
,
h
i
g
h
i
n
d
e
p
e
n
d
e
n
c
e
[0
–
80]
3
.
2
.
Dev
el
o
pin
g
f
uzzy
rule
ba
s
e
T
h
e
f
u
zz
y
r
u
le
b
ase
was
cr
ea
ted
th
r
o
u
g
h
ex
p
er
t
j
u
d
g
m
e
n
t,
in
v
o
l
v
in
g
th
r
ee
m
ath
em
atics
ed
u
ca
tio
n
s
p
ec
ialis
t
s
with
d
o
cto
r
al
d
eg
r
ee
s
an
d
o
v
er
f
iv
e
y
ea
r
s
o
f
e
x
p
er
ien
ce
in
teac
h
in
g
g
eo
m
etr
y
an
d
in
s
tr
u
ctio
n
al
d
esig
n
.
T
h
e
ex
p
e
r
ts
in
d
ep
en
d
e
n
tly
p
r
o
p
o
s
ed
i
n
itial
r
u
le
s
ets
b
ased
o
n
co
m
m
o
n
s
tu
d
e
n
t
er
r
o
r
s
an
d
s
ca
f
f
o
ld
in
g
s
tr
ateg
ies
in
lin
e
with
Pó
ly
a’
s
p
r
o
b
lem
-
s
o
lv
in
g
s
tag
es.
A
c
o
n
s
en
s
u
s
p
r
o
ce
s
s
was
co
n
d
u
cte
d
th
r
o
u
g
h
f
o
cu
s
ed
d
is
cu
s
s
io
n
s
to
r
ef
in
e
a
n
d
v
alid
ate
r
u
les,
en
s
u
r
in
g
c
o
n
s
is
ten
cy
an
d
p
ed
a
g
o
g
ical
r
elev
an
ce
.
T
h
is
ex
p
e
r
t
-
b
ase
d
v
alid
atio
n
p
r
o
ce
s
s
en
h
an
ce
s
th
e
cr
ed
ib
ilit
y
an
d
r
ig
o
r
o
f
th
e
p
r
o
p
o
s
ed
in
f
er
en
ce
r
u
les.
T
h
e
'r
u
l
e
b
a
s
e
'
i
s
t
h
e
m
o
s
t
e
s
s
e
n
t
i
a
l
p
a
r
t
o
f
t
h
e
F
I
S
m
o
d
e
l
.
T
h
e
s
e
r
u
l
e
s
ar
e
m
o
r
e
s
t
r
a
ig
h
tf
o
r
w
ar
d
t
o
f
o
r
m
u
l
a
te
u
s
i
n
g
l
a
n
g
u
ag
e
r
a
th
e
r
t
h
a
n
n
u
m
b
e
r
s
an
d
u
s
u
a
l
ly
a
p
p
e
a
r
a
s
'I
F
-
T
H
E
N
'
s
t
a
t
e
m
e
n
t
s
w
i
t
h
f
u
z
zy
c
o
n
d
i
t
i
o
n
a
l
lo
g
i
c.
I
F
-
T
H
E
N
r
u
l
e
s
a
r
e
co
m
p
o
s
e
d
o
f
t
wo
p
ar
t
s
:
t
h
e
a
n
te
c
e
d
e
n
t
,
w
h
i
ch
r
ep
r
e
s
e
n
t
s
t
h
e
i
n
p
u
t
s
,
a
n
d
th
e
co
n
s
eq
u
en
t
,
wh
i
c
h
in
d
i
c
a
t
e
s
t
h
e
r
e
s
u
l
t
[
3
9
]
.
A
c
t
i
v
at
i
n
g
a
l
l
r
u
l
e
s
th
a
t
h
a
v
e
a
t
r
u
e
p
r
e
m
i
s
e
h
e
lp
s
f
o
r
m
t
h
e
f
u
z
zy
co
n
c
lu
s
i
o
n
s
e
t
.
T
h
e
e
x
t
en
t
to
wh
i
c
h
e
a
ch
r
u
l
e
ac
t
i
v
a
t
e
s
d
e
p
en
d
s
o
n
h
o
w
c
lo
s
e
l
y
th
e
an
t
e
c
ed
e
n
t
m
a
t
c
h
e
s
th
e
i
n
p
u
t.
T
h
i
s
ap
p
r
o
x
i
m
a
t
e
m
a
t
ch
i
n
g
f
o
r
m
s
t
h
e
f
o
u
n
d
a
t
i
o
n
f
o
r
i
n
te
r
p
o
l
a
t
in
g
b
e
t
w
e
e
n
p
o
te
n
t
i
a
l
i
n
p
u
t
s
t
a
t
e
s
a
n
d
r
ed
u
ce
s
t
h
e
n
u
m
b
e
r
o
f
r
u
le
s
r
e
q
u
i
r
ed
to
s
p
e
c
i
f
y
t
h
e
in
p
u
t
-
o
u
tp
u
t
r
e
l
a
ti
o
n
s
h
ip
.
I
F
-
T
H
E
N
r
u
l
e
s
a
r
e
e
s
s
e
n
t
ia
l
b
e
c
au
s
e
t
h
e
y
e
n
ab
l
e
t
h
e
en
c
o
d
i
n
g
o
f
h
u
m
an
ex
p
e
r
t
i
s
e
a
n
d
k
n
o
w
l
ed
g
e
v
i
a
f
u
z
zy
r
u
l
e
s
.
D
i
f
f
e
r
e
n
t
m
e
th
o
d
s
,
in
c
lu
d
in
g
e
x
p
e
r
t
k
n
o
w
le
d
g
e
,
e
x
p
er
t
i
s
e
,
an
d
f
u
z
z
y
m
o
d
e
l
s
,
ca
n
b
e
em
p
l
o
y
ed
to
cr
e
a
t
e
f
u
z
zy
r
u
l
e
s
.
I
n
th
is
s
tep
,
a
s
et
o
f
f
u
zz
y
lin
g
u
is
tic
r
u
les
is
estab
li
s
h
ed
b
a
s
ed
o
n
ex
p
e
r
t
k
n
o
wled
g
e
to
d
ev
elo
p
th
e
r
an
k
in
g
m
o
d
el.
T
h
e
r
u
les
ar
e
estab
lis
h
ed
b
ased
o
n
th
e
d
ec
is
io
n
m
ak
e
r
'
s
p
r
ef
er
en
ce
s
to
e
n
s
u
r
e
s
u
itab
le
r
ec
o
m
m
en
d
atio
n
s
f
o
r
s
ca
f
f
o
ld
in
g
lev
els.
T
h
e
ad
d
itio
n
al
r
eq
u
ir
em
en
t
f
o
r
d
eter
m
i
n
in
g
th
e
s
ca
f
f
o
ld
in
g
lev
el
is
th
e
cr
iter
io
n
o
f
a
m
in
im
u
m
c
o
m
p
o
n
en
t
at
a
m
o
d
er
ate
lev
el
.
B
y
u
n
d
er
s
tan
d
i
n
g
th
e
r
eq
u
ir
em
en
t,
s
tu
d
en
ts
ca
n
m
o
r
e
ea
s
ily
r
ec
eiv
e
a
p
p
r
o
p
r
ia
te
lear
n
in
g
s
u
p
p
o
r
t
b
ased
o
n
t
h
e
d
ef
in
e
d
s
ca
f
f
o
ld
i
n
g
co
m
p
o
n
en
ts
an
d
r
elev
an
t
lev
els.
T
h
e
FIS
s
y
s
tem
,
ac
co
r
d
in
g
to
th
e
r
eq
u
ir
e
m
en
ts
,
is
d
etailed
in
T
ab
le
5
.
T
ab
le
5
.
T
h
e
in
f
er
e
n
ce
r
u
le
b
a
s
e
o
f
th
e
Ma
m
d
a
n
i FI
S m
o
d
el
u
s
ed
to
d
ef
i
n
e
s
ca
f
f
o
ld
in
g
lev
e
ls
R
u
l
e
n
o
IF
TH
EN
Ep
er
dc
l
e
v
e
l
1
W
e
a
k
W
e
a
k
W
e
a
k
B
e
g
i
n
n
e
r
2
W
e
a
k
W
e
a
k
M
o
d
e
r
a
t
e
B
e
g
i
n
n
e
r
3
W
e
a
k
W
e
a
k
S
t
r
o
n
g
B
e
g
i
n
n
e
r
4
W
e
a
k
M
o
d
e
r
a
t
e
W
e
a
k
B
e
g
i
n
n
e
r
5
W
e
a
k
M
o
d
e
r
a
t
e
M
o
d
e
r
a
t
e
A
d
v
a
n
c
e
6
W
e
a
k
M
o
d
e
r
a
t
e
S
t
r
o
n
g
A
d
v
a
n
c
e
7
W
e
a
k
S
t
r
o
n
g
W
e
a
k
B
e
g
i
n
n
e
r
8
W
e
a
k
S
t
r
o
n
g
M
o
d
e
r
a
t
e
A
d
v
a
n
c
e
9
W
e
a
k
S
t
r
o
n
g
S
t
r
o
n
g
I
n
d
e
p
e
n
d
e
n
t
10
M
o
d
e
r
a
t
e
W
e
a
k
W
e
a
k
B
e
g
i
n
n
e
r
⋮
⋮
⋮
⋮
⋮
⋮
⋮
⋮
⋮
⋮
27
S
t
r
o
n
g
S
t
r
o
n
g
S
t
r
o
n
g
H
i
g
h
i
n
d
e
p
e
n
d
e
n
c
e
3
.
3
.
Def
uzzif
ica
t
io
n
On
ce
th
e
FIS
p
r
o
ce
s
s
co
n
clu
d
es,
th
e
d
ef
u
zz
if
icatio
n
s
te
p
tr
an
s
f
o
r
m
s
th
e
o
u
tp
u
t
in
to
p
r
ec
is
e,
n
u
m
er
ical
v
alu
es.
Var
io
u
s
tech
n
iq
u
es in
f
u
zz
y
lo
g
ic,
lik
e
th
e
ce
n
tr
o
id
,
h
eig
h
t,
an
d
m
ea
n
-
m
ax
m
eth
o
d
s
,
ca
n
b
e
u
s
ed
f
o
r
d
e
f
u
zz
if
icatio
n
[
4
0
]
.
T
h
is
p
r
o
b
lem
em
p
lo
y
s
th
e
c
en
tr
o
id
m
eth
o
d
to
d
e
r
iv
e
a
p
r
ec
is
e
o
u
tp
u
t
v
alu
e
f
r
o
m
t
h
e
f
u
zz
y
o
u
tp
u
t
s
et
p
r
o
d
u
ce
d
d
u
r
in
g
th
e
p
r
ev
io
u
s
in
f
er
en
ce
p
r
o
ce
s
s
.
T
h
er
ef
o
r
e,
th
e
v
al
u
e
o
f
z
is
d
eter
m
in
ed
u
s
in
g
th
e
ce
n
tr
o
id
m
eth
o
d
.
T
h
e
o
u
t
p
u
t
f
o
r
ass
ess
in
g
s
ca
f
f
o
ld
in
g
lev
els
in
clu
d
es
f
o
u
r
f
u
zz
y
s
ets:
b
eg
in
n
er
,
ad
v
an
ce
d
,
in
d
ep
en
d
en
t,
a
n
d
h
ig
h
in
d
ep
en
d
en
ce
lev
el
.
T
h
e
f
u
zz
y
d
e
cisi
o
n
in
d
ex
is
ca
lcu
lated
b
y
r
ec
alcu
latin
g
th
e
d
ec
is
io
n
lev
el
p
er
ce
n
tag
e
b
ased
o
n
th
e
o
b
tain
ed
c
r
is
p
d
ec
i
s
io
n
v
alu
e.
T
h
e
c
o
n
s
tr
u
cted
i
n
f
er
en
ce
s
y
s
tem
is
u
s
ed
to
o
b
tain
th
e
f
u
zz
y
d
ec
is
i
o
n
in
d
e
x
o
u
t
p
u
t
as
(
1
1
)
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
2
5
2
-
8
9
3
8
I
n
t J Ar
tif
I
n
tell
,
Vo
l.
15
,
No
.
4
,
Au
g
u
s
t 2
0
2
6
:
3
2
8
6
-
3
2
9
8
3294
(
)
=
{
1
,
<
10
30
−
20
,
10
≤
<
30
0
,
≥
30
(
)
=
{
0
,
<
10
−
10
20
,
10
≤
<
30
50
−
20
,
30
≤
<
50
0
,
≥
50
(
)
=
{
0
,
<
30
−
30
20
,
30
≤
<
50
70
−
20
,
50
≤
<
70
0
,
≥
70
(
)
=
{
0
,
<
50
−
50
20
,
50
≤
<
70
1
,
≥
70
(
1
1
)
3
.
4
.
I
m
ple
m
ent
a
t
io
n o
f
M
a
m
da
ni F
I
S in Sprea
d
s
heet
T
h
e
in
s
tr
u
m
en
t
c
o
n
s
is
ts
o
f
th
e
in
ter
ac
tio
n
b
etwe
en
t
h
e
p
r
i
m
ar
y
an
d
s
ev
er
al
au
x
iliar
y
s
p
r
ea
d
s
h
ee
ts
.
T
h
e
p
r
im
ar
y
s
p
r
ea
d
s
h
ee
t
p
r
o
v
id
es
a
s
im
u
latio
n
f
o
r
d
eter
m
in
in
g
th
e
lev
el
o
f
s
ca
f
f
o
ld
in
g
b
ased
o
n
s
tu
d
en
ts
'
p
er
f
o
r
m
an
ce
in
s
o
lv
in
g
g
eo
m
etr
y
p
r
o
b
lem
s
.
Me
a
n
wh
ile,
th
e
au
x
iliar
y
s
p
r
ea
d
s
h
ee
ts
co
n
tain
ca
lcu
latio
n
s
r
elate
d
to
th
e
d
if
f
e
r
en
t
co
m
p
o
n
en
ts
o
f
s
ca
f
f
o
ld
in
g
an
d
c
o
r
r
esp
o
n
d
in
g
le
v
els,
s
er
v
in
g
as
d
ata
s
o
u
r
ce
s
f
o
r
th
e
p
r
im
ar
y
s
p
r
ea
d
s
h
ee
t.
T
h
is
im
p
lem
en
tatio
n
was
ca
r
r
ied
o
u
t
o
n
3
0
ad
d
itio
n
al
ca
s
es,
as
s
h
o
wn
in
T
ab
le
6
.
T
h
e
s
u
b
ject
d
ata
is
co
llected
f
r
o
m
p
er
s
o
n
al
in
f
o
r
m
atio
n
r
ela
ted
to
s
tu
d
en
ts
'
co
g
n
itiv
e
ab
ilit
ies,
s
ca
f
f
o
ld
in
g
elem
en
ts
,
an
d
p
r
o
b
lem
-
s
o
lv
in
g
s
k
ills
.
T
h
is
in
f
o
r
m
atio
n
is
u
s
ed
as
in
p
u
t
to
d
eter
m
in
e
th
e
ap
p
r
o
p
r
iate
lev
el
o
f
s
ca
f
f
o
ld
in
g
to
s
u
p
p
o
r
t le
ar
n
in
g
n
ee
d
s
an
d
en
h
a
n
ce
p
r
o
b
lem
-
s
o
lv
in
g
ab
ilit
ies.
T
ab
le
6
.
I
m
p
lem
en
tatio
n
o
f
M
am
d
an
i FI
S in
f
er
e
n
ce
r
u
le
b
ase
f
o
r
s
ca
f
f
o
ld
in
g
le
v
el
d
eter
m
i
n
atio
n
S
u
b
j
e
c
t
I
n
p
u
t
O
u
t
p
u
t
l
e
v
e
l
ep
er
dc
S1
13
16
00
A
d
v
a
n
c
e
S2
09
25
05
A
d
v
a
n
c
e
S3
09
30
06
A
d
v
a
n
c
e
S4
17
20
05
A
d
v
a
n
c
e
S5
04
35
14
A
d
v
a
n
c
e
S6
08
35
11
A
d
v
a
n
c
e
S7
15
35
14
I
n
d
e
p
e
n
d
e
n
t
S8
20
40
12
H
i
g
h
i
n
d
e
p
e
n
d
e
n
c
e
⋮
⋮
⋮
⋮
⋮
S
2
7
06
19
03
B
e
g
i
n
n
e
r
S
2
8
05
31
07
A
d
v
a
n
c
e
S
2
9
14
39
11
I
n
d
e
p
e
n
d
e
n
t
S
3
0
16
30
13
I
n
d
e
p
e
n
d
e
n
t
3
.
5
.
Dis
cus
s
io
n
A
d
ec
is
io
n
s
u
p
p
o
r
t
s
y
s
tem
f
o
r
d
eter
m
in
in
g
s
ca
f
f
o
ld
i
n
g
lev
els
is
im
p
lem
en
ted
u
s
in
g
v
a
r
io
u
s
co
m
p
u
tatio
n
al
m
eth
o
d
s
.
T
h
is
s
y
s
tem
,
wh
ich
u
s
es
th
e
Ma
m
d
an
i
FIS
m
eth
o
d
,
is
s
u
itab
le
f
o
r
ed
u
ca
ti
o
n
al
s
ettin
g
s
b
ec
au
s
e
it
ca
n
m
an
ag
e
u
n
ce
r
tain
ty
an
d
am
b
i
g
u
ity
i
n
s
tu
d
en
t
p
er
f
o
r
m
an
ce
d
ata.
Fu
zz
y
lo
g
ic
h
as
b
ee
n
u
tili
ze
d
in
ed
u
ca
tio
n
t
o
ass
is
t
d
ec
is
io
n
-
m
ak
in
g
p
r
o
ce
s
s
es
lik
e
s
ch
o
lar
s
h
ip
s
elec
tio
n
,
ac
cr
ed
itatio
n
ass
ess
m
en
t,
an
d
p
r
o
g
r
am
o
r
m
ajo
r
s
elec
tio
n
,
s
h
o
win
g
th
e
f
lex
i
b
ilit
y
an
d
r
elev
a
n
ce
in
co
m
p
le
x
h
u
m
an
-
ce
n
ter
ed
d
o
m
ain
s
[
4
1
]
–
[
4
3
]
.
T
h
e
p
r
i
m
ar
y
b
en
ef
it
o
f
th
e
Ma
m
d
a
n
i
ap
p
r
o
ac
h
is
its
ca
p
ac
ity
t
o
co
n
v
er
t
q
u
alitativ
e
p
ed
ag
o
g
ical
in
s
ig
h
ts
in
to
u
n
d
er
s
tan
d
ab
le
f
u
zz
y
r
u
les,
w
h
ich
p
r
o
d
u
ce
r
ec
o
m
m
en
d
atio
n
s
tailo
r
ed
to
th
e
co
n
tex
t.
Ho
wev
e
r
,
th
e
s
y
s
tem
d
o
es
n
o
t
r
ep
lace
teac
h
er
j
u
d
g
m
e
n
t
b
u
t
o
p
er
atio
n
alize
s
th
e
co
n
ce
p
t
in
to
a
tr
an
s
p
ar
en
t d
ec
is
io
n
-
m
ak
in
g
f
r
am
ewo
r
k
.
Ma
m
d
an
i
FIS
was
u
s
ed
to
d
eter
m
in
e
ap
p
r
o
p
r
iate
s
ca
f
f
o
l
d
in
g
lev
els
b
ased
o
n
s
tu
d
en
ts
’
er
r
o
r
p
atter
n
s
in
s
o
lv
in
g
g
eo
m
etr
y
p
r
o
b
lem
s
.
Ma
m
d
an
i
FIS
tr
an
s
lated
p
atter
n
s
o
f
s
tu
d
en
t
er
r
o
r
s
ac
r
o
s
s
Pó
ly
a’
s
p
r
o
b
lem
s
o
lv
in
g
s
tag
es
in
to
d
if
f
e
r
en
tia
ted
s
ca
f
f
o
ld
in
g
lev
els.
T
h
e
s
y
s
tem
o
p
er
ates
th
r
o
u
g
h
a
s
tr
u
c
tu
r
ed
s
eq
u
en
ce
o
f
s
tag
es,
in
clu
d
in
g
f
u
zz
i
f
icatio
n
o
f
in
p
u
t
v
ar
iab
les,
in
f
e
r
en
ce
u
s
in
g
ex
p
er
t
-
d
ef
in
ed
f
u
zz
y
r
u
le
s
,
r
u
le
ag
g
r
e
g
atio
n
,
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Ar
tif
I
n
tell
I
SS
N:
2252
-
8
9
3
8
Dete
r
min
in
g
s
tu
d
en
t sca
ffo
ld
in
g
leve
ls
in
g
eo
metry
p
r
o
b
lem
-
s
o
lvin
g
:
a
f
u
z
z
y
…
(
Yu
n
ia
r
I
k
a
P
u
tr
i P
r
a
n
ya
ta
)
3295
an
d
d
ef
u
zz
if
icatio
n
to
p
r
o
d
u
ce
cr
is
p
s
ca
f
f
o
ld
in
g
lev
el
o
u
tp
u
t
s
.
T
h
is
p
r
o
ce
s
s
allo
ws
d
iv
er
s
e
p
atter
n
s
o
f
s
tu
d
en
t
er
r
o
r
s
in
lin
e
with
Pó
l
y
a’
s
p
r
o
b
lem
-
s
o
lv
in
g
s
tag
es
to
b
e
m
a
p
p
ed
in
to
m
ea
n
in
g
f
u
l
in
s
tr
u
cti
o
n
al
s
u
p
p
o
r
t
lev
els.
T
h
er
ef
o
r
e,
th
e
s
y
s
tem
p
r
o
v
id
es
a
tr
an
s
p
ar
en
t
an
d
in
t
er
p
r
etab
le
m
ec
h
a
n
is
m
f
o
r
co
n
n
ec
tin
g
s
tu
d
e
n
t
p
er
f
o
r
m
an
ce
ch
a
r
ac
ter
is
tics
to
s
ca
f
f
o
ld
in
g
r
ec
o
m
m
e
n
d
atio
n
s
.
T
h
e
m
ain
o
b
jectiv
e
o
f
in
teg
r
atin
g
Ma
m
d
an
i
d
ec
is
io
n
s
u
p
p
o
r
t
s
y
s
tem
is
to
s
u
p
p
o
r
t
p
e
r
s
o
n
alize
d
lear
n
in
g
b
y
b
alan
cin
g
in
s
tr
u
ctio
n
al
s
ca
f
f
o
ld
in
g
with
ac
t
u
al
p
r
o
b
lem
-
s
o
lv
in
g
n
ee
d
s
.
T
h
e
s
y
s
tem
ass
i
s
ts
teac
h
er
s
in
d
eliv
er
i
n
g
s
u
p
p
o
r
t
b
y
class
if
y
in
g
s
tu
d
en
ts
in
to
d
if
f
er
en
t
s
ca
f
f
o
ld
in
g
lev
els,
e
n
h
an
cin
g
s
tu
d
en
ts
’
in
d
ep
en
d
en
ce
an
d
s
tr
ateg
ic
th
in
k
in
g
.
T
ea
ch
e
r
s
ca
n
m
o
d
if
y
o
r
e
x
p
an
d
th
e
r
u
le
b
ase
to
ac
co
m
m
o
d
ate
s
p
ec
if
ic
cu
r
r
icu
lu
m
o
b
jectiv
es,
in
s
titu
tio
n
al
r
eq
u
ir
em
en
ts
,
o
r
s
tu
d
en
t
c
h
ar
ac
ter
is
tics
.
T
h
e
s
ca
f
f
o
ld
in
g
r
ec
o
m
m
en
d
atio
n
s
ca
n
b
e
r
e
f
in
ed
th
r
o
u
g
h
ad
d
itio
n
al
r
u
les
o
r
alter
n
ativ
e
p
ar
am
eter
s
ettin
g
s
b
y
lev
er
ag
in
g
th
e
ad
v
an
tag
es o
f
f
u
zz
y
lo
g
ic,
en
a
b
lin
g
th
e
s
y
s
tem
to
f
u
n
ctio
n
as a
cu
s
to
m
izab
le
d
ec
is
io
n
-
s
u
p
p
o
r
t to
o
l r
ath
er
th
an
a
r
ig
id
ev
alu
ativ
e
m
ec
h
a
n
is
m
.
T
h
e
s
p
r
ea
d
s
h
ee
t
-
b
ased
im
p
lem
en
tatio
n
s
h
o
ws
th
at
th
e
p
r
o
p
o
s
ed
s
y
s
tem
is
p
r
ac
tically
f
ea
s
ib
le
an
d
ac
ce
s
s
ib
le,
allo
win
g
teac
h
er
s
an
d
ass
es
s
m
en
t
team
s
to
ap
p
ly
th
e
co
n
ce
p
t
with
o
u
t
r
eq
u
ir
in
g
ad
v
an
ce
d
tech
n
ical
in
f
r
astru
ctu
r
e.
I
n
r
ea
l
in
s
tr
u
ctio
n
al
s
ettin
g
s
,
teac
h
er
s
m
ak
e
r
ap
id
in
s
tr
u
ctio
n
a
l
ad
ju
s
tm
en
ts
u
n
d
e
r
co
g
n
itiv
e
l
o
ad
.
T
h
e
d
ec
is
io
n
s
u
p
p
o
r
t
s
y
s
tem
h
as
th
e
p
o
ten
tial
t
o
allev
iate
th
e
b
u
r
d
en
b
y
ex
ter
n
alizin
g
d
ia
g
n
o
s
tic
r
ea
s
o
n
in
g
p
r
o
ce
s
s
es,
en
ab
lin
g
te
ac
h
er
s
to
co
n
ce
n
tr
ate
o
n
p
ed
ag
o
g
ical
in
ter
ac
tio
n
r
ath
er
th
an
o
n
s
u
b
jectiv
e
ev
a
lu
ativ
e
ju
d
g
m
en
ts
[
4
1
]
.
Ho
w
ev
er
,
class
r
o
o
m
in
teg
r
atio
n
o
f
th
e
s
y
s
tem
is
n
o
t
in
h
er
en
tly
g
u
ar
an
teed
.
T
ea
ch
e
r
s
m
u
s
t
r
ec
eiv
e
p
ed
ag
o
g
ical
tr
ain
in
g
to
in
ter
p
r
et
s
ca
f
f
o
ld
in
g
class
if
icatio
n
s
as
f
o
r
m
ativ
e
g
u
i
d
an
ce
r
ath
er
th
an
as
p
r
escr
ip
tiv
e
lab
els.
I
n
th
e
ab
s
en
ce
o
f
th
e
tr
ain
in
g
,
t
h
e
s
y
s
tem
m
ay
b
e
m
is
ap
p
r
o
p
r
iated
as
a
s
u
m
m
a
tiv
e
g
r
ad
in
g
in
s
tr
u
m
en
t,
wh
i
ch
co
n
tr
ad
icts
th
e
d
ev
elo
p
m
en
tal
an
d
ad
ap
tiv
e
n
atu
r
e
o
f
s
ca
f
f
o
ld
in
g
[
2
1
]
.
T
h
er
ef
o
r
e,
s
u
cc
ess
f
u
l
ad
o
p
ti
o
n
o
f
th
e
p
r
o
p
o
s
ed
s
y
s
tem
is
d
ep
en
d
en
t
o
n
p
r
o
f
ess
io
n
al
d
ev
elo
p
m
en
t
in
i
tiativ
es
th
at
ex
p
licitly
co
n
n
ec
t
s
y
s
tem
o
u
tp
u
ts
to
r
esp
o
n
s
iv
e
an
d
ad
ap
tiv
e
in
s
tr
u
ctio
n
al
p
r
ac
tices
[
4
2
]
.
T
h
e
s
y
s
tem
o
u
tp
u
ts
wer
e
d
escr
ip
tiv
ely
co
m
p
ar
ed
with
s
tu
d
en
ts
'
o
b
s
er
v
ed
p
r
o
b
lem
-
s
o
lv
in
g
b
eh
av
io
r
s
an
d
p
er
f
o
r
m
an
ce
p
atter
n
s
d
u
r
in
g
g
eo
m
etr
y
in
s
tr
u
ctio
n
t
o
ex
am
in
e
th
e
r
elev
a
n
ce
o
f
t
h
e
g
e
n
er
ated
s
ca
f
f
o
ld
in
g
r
ec
o
m
m
en
d
atio
n
s
.
T
h
e
an
aly
s
is
s
h
o
ws
a
co
n
s
is
ten
cy
b
etwe
en
th
e
r
ec
o
m
m
en
d
ed
s
ca
f
f
o
ld
in
g
lev
els
an
d
s
tu
d
en
ts
’
lear
n
in
g
ch
ar
ac
ter
is
t
ics.
T
h
is
r
esu
lt
s
u
p
p
o
r
ts
th
e
v
iew
th
at
ef
f
ec
tiv
e
in
s
tr
u
ctio
n
al
s
u
p
p
o
r
t
s
h
o
u
ld
b
e
d
iag
n
o
s
is
-
d
r
iv
en
[
4
3
]
.
Stu
d
en
t
s
ca
teg
o
r
ized
at
lo
wer
s
ca
f
f
o
l
d
in
g
lev
els
ten
d
ed
t
o
ex
h
i
b
it
f
r
eq
u
en
t
co
n
ce
p
tu
al
m
is
u
n
d
er
s
tan
d
in
g
s
a
n
d
p
r
o
ce
d
u
r
al
er
r
o
r
s
,
wh
ile
t
h
o
s
e
class
if
ied
at
h
ig
h
er
i
n
d
ep
e
n
d
en
ce
le
v
els
r
ep
o
r
te
d
m
o
r
e
co
h
er
en
t
s
o
lu
tio
n
s
tr
ateg
ies,
ef
f
ec
tiv
e
s
elf
-
m
o
n
ito
r
in
g
,
an
d
r
ef
lectiv
e
p
r
o
b
lem
-
s
o
lv
in
g
b
eh
av
io
r
s
.
T
h
is
co
r
r
esp
o
n
d
en
ce
s
u
g
g
ests
th
at
th
e
p
r
o
p
o
s
ed
Ma
m
d
a
n
i
FIS
p
r
o
d
u
ce
s
r
ec
o
m
m
e
n
d
ati
o
n
s
p
ed
ag
o
g
ically
m
ea
n
in
g
f
u
l a
n
d
b
alan
ce
d
with
s
tu
d
en
ts
’
ac
tu
al
lear
n
in
g
n
ee
d
s
.
T
h
e
im
p
lem
en
tatio
n
o
f
th
e
s
y
s
tem
in
r
ea
l
class
r
o
o
m
en
v
ir
o
n
m
e
n
ts
p
r
esen
ts
o
p
p
o
r
tu
n
ities
an
d
ch
allen
g
es.
T
ea
ch
e
r
s
r
eq
u
i
r
e
t
ar
g
eted
tr
ain
i
n
g
t
o
in
ter
p
r
et
s
y
s
tem
o
u
tp
u
ts
an
d
i
n
teg
r
ate
t
h
e
r
ec
o
m
m
e
n
d
atio
n
s
ef
f
ec
tiv
ely
in
to
in
s
tr
u
ctio
n
al
d
ec
is
io
n
-
m
ak
in
g
.
Mo
r
eo
v
e
r
,
s
tu
d
en
t
d
iv
er
s
ity
in
ter
m
s
o
f
lear
n
in
g
s
ty
les,
cu
ltu
r
al
b
ac
k
g
r
o
u
n
d
s
,
an
d
p
r
io
r
k
n
o
wled
g
e
n
ec
ess
itates f
lex
ib
ilit
y
in
ap
p
ly
in
g
s
ca
f
f
o
ld
in
g
r
u
les.
T
h
e
r
u
le
b
a
s
e
s
h
o
u
l
d
b
e
t
r
e
a
t
e
d
a
s
a
d
a
p
t
a
b
l
e
r
a
t
h
e
r
t
h
a
n
u
n
i
v
e
r
s
al
.
T
h
e
f
l
e
x
i
b
i
l
i
t
y
o
f
f
u
z
z
y
l
o
g
ic
e
n
a
b
l
es
c
o
n
t
e
x
t
u
a
l
ca
lib
r
atio
n
,
allo
win
g
s
tu
d
en
ts
t
o
r
ef
in
e
m
em
b
er
s
h
ip
f
u
n
ctio
n
s
o
r
r
u
les
ac
co
r
d
in
g
to
class
r
o
o
m
ch
ar
a
cter
is
tics
[
3
4
]
.
T
h
is
ad
ap
tab
ilit
y
p
o
s
itio
n
s
th
e
s
y
s
tem
as
a
co
llab
o
r
ativ
e
p
ed
ag
o
g
ical
in
s
tr
u
m
en
t
r
ath
er
th
an
a
f
ix
e
d
in
tellig
en
t
tu
to
r
.
Fu
t
u
r
e
e
x
ten
s
io
n
s
o
f
t
h
e
s
y
s
tem
in
co
r
p
o
r
ate
ad
a
p
tiv
e
m
ec
h
an
is
m
s
th
at
r
esp
o
n
d
d
y
n
am
ically
to
ch
an
g
es
in
s
tu
d
en
t
p
er
f
o
r
m
a
n
ce
an
d
ex
ten
d
th
e
s
y
s
tem
’
s
ap
p
licati
o
n
to
ad
d
itio
n
al
m
ath
e
m
atica
l
d
o
m
ain
s
b
ey
o
n
d
g
eo
m
etr
y
,
s
u
ch
as
alg
eb
r
a
o
r
ca
lcu
lu
s
.
T
h
e
cr
o
s
s
-
d
o
m
ai
n
ex
ten
s
io
n
s
en
ab
le
in
v
esti
g
atio
n
in
to
wh
eth
er
o
b
s
er
v
ed
s
ca
f
f
o
l
d
in
g
p
atter
n
s
ar
e
d
o
m
ain
-
s
p
ec
if
ic
o
r
r
ef
le
ct
s
tab
le
s
tu
d
en
t
ch
ar
ac
ter
is
ti
cs,
co
n
tr
ib
u
tin
g
to
b
r
o
ad
e
r
th
eo
r
etica
l
u
n
d
er
s
tan
d
in
g
s
o
f
a
d
ap
tiv
e
in
s
tr
u
cti
o
n
.
Ma
m
d
a
n
i
FIS
d
em
o
n
s
tr
ates
p
o
ten
tial
an
d
ef
f
ec
tiv
en
ess
in
in
teg
r
atin
g
d
ec
is
io
n
s
u
p
p
o
r
t
s
y
s
tem
s
[
4
4
]
,
[
4
5
]
.
T
h
e
r
esu
lts
s
h
o
w
th
at
th
e
s
y
s
tem
h
as
p
o
ten
tial
as
a
d
ec
is
io
n
s
u
p
p
o
r
t
to
o
l
f
o
r
p
e
r
s
o
n
alize
d
s
ca
f
f
o
ld
in
g
in
m
ath
em
atics
ed
u
ca
t
io
n
.
T
h
e
p
r
o
p
o
s
ed
ap
p
r
o
ac
h
co
n
tr
ib
u
tes
to
m
o
r
e
ad
ap
tiv
e,
tr
an
s
p
ar
en
t,
an
d
co
n
tex
t
-
awa
r
e
in
s
tr
u
ctio
n
al
s
u
p
p
o
r
t
to
im
p
r
o
v
e
s
tu
d
en
ts
’
p
r
o
b
lem
-
s
o
lv
in
g
s
k
ills
an
d
lear
n
in
g
r
esu
lts
b
y
co
n
n
ec
tin
g
p
ed
ag
o
g
ical
th
eo
r
y
with
in
tellig
en
t
s
y
s
tem
d
esig
n
.
Desp
ite
th
e
p
r
o
m
is
in
g
r
esu
lts
,
s
ev
er
al
lim
itatio
n
s
s
h
o
u
ld
b
e
ac
k
n
o
wled
g
ed
.
T
h
e
f
u
zz
y
r
u
le
b
ase
d
ep
en
d
s
o
n
ex
p
er
t
ju
d
g
m
e
n
t,
wh
ich
m
ay
in
tr
o
d
u
ce
s
u
b
jectiv
ity
an
d
lim
it
th
e
g
en
er
aliza
b
ilit
y
o
f
th
e
s
y
s
tem
ac
r
o
s
s
d
if
f
er
en
t
in
s
tr
u
ctio
n
al
co
n
tex
ts
o
r
s
tu
d
en
t
p
o
p
u
latio
n
s
.
T
h
e
c
u
r
r
en
t
im
p
lem
en
tati
o
n
is
b
ased
o
n
s
tatic
in
p
u
t
d
ata
an
d
d
o
es
n
o
t
ac
co
u
n
t
f
o
r
d
y
n
am
ic
ch
an
g
es
in
lear
n
in
g
tr
ajec
to
r
ies.
Ad
d
r
ess
in
g
th
e
lim
itatio
n
s
r
eq
u
ir
es
f
u
tu
r
e
s
tu
d
ies
th
at
in
co
r
p
o
r
ate
lo
n
g
itu
d
in
al
d
ata,
a
d
ap
tiv
e
r
u
le
-
u
p
d
atin
g
m
ec
h
a
n
is
m
s
,
an
d
em
p
ir
ical
v
alid
atio
n
u
s
in
g
q
u
an
titativ
e
l
ea
r
n
in
g
o
u
tco
m
e
m
ea
s
u
r
es.
4.
CO
NCLU
SI
O
N
T
h
e
d
ec
is
io
n
s
u
p
p
o
r
t
s
y
s
tem
f
o
r
d
eter
m
i
n
in
g
s
ca
f
f
o
ld
in
g
ca
n
b
e
ad
o
p
ted
t
o
m
ak
e
i
n
f
o
r
m
e
d
d
ec
is
io
n
s
ab
o
u
t
t
h
e
ap
p
r
o
p
r
iate
lev
el
o
f
s
u
p
p
o
r
t
f
o
r
s
tu
d
e
n
ts
wo
r
k
i
n
g
o
n
g
eo
m
etr
y
p
r
o
b
lem
s
.
T
h
is
s
y
s
tem
en
s
u
r
es
th
at
Evaluation Warning : The document was created with Spire.PDF for Python.