Examples of the Implementation of Fuzzy Models in Tourism in the South Moravian Region - Geoinformatics for Intelligent Transportation - page 172

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