Information Technology Reference
In-Depth Information
⎧
3
a
⎛
⎞
m
0
0
≤
x
≤
⎜
⎝
1
−
⎟
⎠
;
⎪
2
⎪
⎛
a
⎞
⎪
⎜
1
−
m
−
x
⎟
⎪
⎛
3
a
⎞
⎛
a
⎞
2
()
⎜
⎟
μ
x
=
L
,
1
−
m
<
x
≤
1
−
m
;
⎨
⎜
⎝
⎟
⎠
⎜
⎝
⎟
⎠
m
⎜
⎜
a
⎟
⎟
2
2
⎪
m
⎪
⎝
⎠
⎪
a
⎛
⎞
1
1
−
m
<
x
≤
1
.
⎜
⎝
⎟
⎠
⎪
2
⎩
()
Fig. 2.1 shows membership functions of term
for a special case
;
X
L
x
= 1
−
x
m
x
(membership functions of
T
-numbers). The special attention is given to
this special case because of large number of application of
T
-numbers and normal
triangular numbers in applied researches.
0
≤
≤
1
()
a
≤
a
Fig. 2.1
Membership function
μ
x
under conditions: a —
, b —
m
m
−
1
m
a
>
a
m
m
−
1
a
>
a
2.
If
, then
m
m
−