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Mamdani
'
s method (COS-TM-TM, COM-TM-TM)
; l D j ðÞ
; l D j ðÞ
k
j ¼ 1 T M T M w 1j ; w 2j
k
j ¼ 1 min min w 1j ; w 2j
l D 0 ðÞ¼
¼
max
max
Larsen
'
s method (COS-TP-TM)
; l D j ðÞ
l D j ðÞ
k
j ¼
k
j ¼
l D 0 ðÞ¼
max
1 T P T M w 1j ; w 2j
¼
max
min w 1j ; w 2j
1
7.2 Mamdani
s Method (COS-TM-TM)
'
Considering evaluation of the road surface and reasoning of conclusion rule-by-
rule, we will choose (COS-TM-TM) the centroid of sums which means calculation.
Y l D j ðÞ ydy
P
1 j 6
y CoS
D j ¼
P
Y l D j ðÞ dy
1 j 6
Y l D 0 1 ðÞ ydy þ Y l D 0 2 ðÞ ydy þ Y l D 0 3 ðÞ ydy þ Y l D 0 4 ðÞ ydy þ Y l D 0 5 ðÞ ydy þ Y l D 0 6 ðÞ ydy
Y l D 0 1
ðÞ dy þ Y l D 0 2
ðÞ dy þ Y l D 0 3
ðÞ dy þ Y l D 0 4
ðÞ dy þ Y l D 0 5 ðÞ dy þ Y l D 0 6
¼
ðÞ dy
The total weight of the j-th rule w j is the minimum of the particular weights of
the premises (roads, slope) w 1j ; w 2j in this rule (simply signed w). The membership
function of the conclusion of the j-th rule is presented as
.
l D j ðÞ¼
min w j ; l D j ðÞ
The membership
l D j ðÞ
is simply denoted
l ðÞ
.
In the
first and the second rule we evaluate small dif
culty D 1 (Fig. 12 ).
2
w
+
3
3
y
3
2
9
3
2
w
y
dy
+
+
y
dy
=
w
3
w
+
w
2
2
3
2
0
2
w
+
3
and
2
w
+
3
3
y
3
2
w
dy
+
+
dy
=
w
+
3
w
2
2
0
2
w
+
3
Fig. 12 Membership function for small dif culty
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