Examples of the Implementation of Fuzzy Models in Tourism in the South Moravian Region - Geoinformatics for Intelligent Transportation - page 173

2 w + 1 − 2 w + 5

y 1

⊛ ⊞

∫ ∫

⊝ − ⊠ y dy + w y dy +

2 2

1 2 w + 1

5

y 5

⊛ ⊞

∫ +

2

+ ⊝ − + ⊠ y dy = − 6 w + 12 w

2 2

− 2 w 5

and

2 w + 1 − 2 w + 5

y 1

⊛ ⊞

∫ ∫

− dy + w dy +

⊝ ⊠

2 2

1 2 w + 1

5

y 5

⊛ ⊞

∫ +

2

+ − + dy = − 2 w + 4 w

⊝ ⊠

2 2

− 2 w 5

Fig. 13 Membership function for intermediate difficulty

In the third and the fourth rule we evaluate intermediate dif culty D 2 (Fig. 13 ).

In the fifth and the sixth rule we evaluate hard dif culty D 3 (Fig. 14 ).

Z

ydy þ

Z

2w þ 3 6

2 3

2

2
3 w

27
2

3 2

wydy ¼ 3w þ

3 2w þ 3

and

Z

dy þ

Z

2w þ 3 6

2 3

2

2

wdy ¼ w þ 3w

3 2w þ 3

2 w + 3 6

y 3 2 27

⊛ ⊞

∫ ∫

3 2

− y dy + w y dy = − w − 3 w +

⊝ ⊠

2 2 3 2

3 2 w + 3

and

2 w + 3 6

y 3

⊛ ⊞

∫ ∫

2

⊝ − ⊠ dy + w dy = − w + 3 w

2 2

3 2 w + 3

Fig. 14 Membership function for hard difficulty