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()
μ
x
i
=
1
Then, membership functions
,
for terms “very low”, "low",
i
"average",
"high",
“very
high”
are
T
-numbers
and
look
like:
() (
)
() (
)
() (
)
μ
x
=
0
11
;
02
;
05
μ
x
=
−
1
−
0
005
;
005
μ
x
=
0
09
;
005
;
02
;
;
;
3
1
2
() (
)
() (
)
;
, accordingly.
μ
x
=
0
μ
x
=
0
,
35
;
0
45
;
,
05
;
,
05
5
4
2.
5 For mali zatio n of Li ng uistic Val ues of C haracteristics
2.5 Formalization of Linguistic Values of Characteristics on the
Basis of Direct Inquiry of a Single Expert Regarding a
Partition of Universal Set
Let, for any reasons, an expert has difficulties in defining typical intervals for
COSS terms, but he/she can divide universal set into disjoint intervals each
mapped to one of terms and being a set of 0.5-level of the fuzzy number
corresponding to this term. Let us assume that the fuzzy numbers corresponding to
COSS terms are
2.
5 For mali zatio n of Li ng uistic Val ues of C haracteristics
Form alizati on of Lin guis tic Values of Characteristics
-numbers, and the side condition (1*) is satisfied for func
tion
s
Λ
()
()
()
μ
x
l
=
1
m
L
x
,
R
x
. Let us denote membership functions of terms
X
as
,
.
l
Let us denote length of the interval corresponding to term
X
through
m
[
]
∑
=
c
,
c
=
b
−
a
;
U
=
a
,
b
.
l
l
l
1
()
Let us construct membership functions
μ
x
as curvilinear trapezoids with
l
c
midlines equal to
c
≤
c
1.
If
, then
m
m
−
1
⎧
3
c
⎛
⎞
m
0
a
≤
x
≤
⎜
⎝
b
−
⎟
⎠
;
⎪
2
⎪
c
⎛
⎞
⎪
b
−
m
−
x
⎜
⎟
⎪
3
c
c
⎛
⎞
⎛
⎞
2
()
⎜
⎟
μ
x
=
L
,
b
−
m
<
x
≤
b
−
m
;
⎜
⎝
⎟
⎠
⎜
⎝
⎟
⎠
⎨
m
⎜
⎜
c
⎟
⎟
2
2
⎪
m
⎪
⎝
⎠
⎪
c
⎛
⎞
1
b
−
m
<
x
≤
b
.
⎜
⎝
⎟
⎠
⎪
2
⎩
2.
If
c
>
c
, then
m
m
−
1
