Methods of Expert Information Formalization Based on Complete Orthogonal Semantic Spaces - Expert Fuzzy Information Processing - page 65

⎧

1 − b

1 0 ≤ x ≤

1

;

⎪

a

⎪ ⎪

1

b 1 − b b

()

μ x = a x + a

3

,

1

< x ≤ −

3

;

⎨

1 1 1

a a a

⎪

3 1 3

b

⎪

3

0 − < x ≤ 1

⎪

a

⎩

3

1 − b

⎧

0 0 ≤ x ≤

1

;

⎪

a

⎪ ⎪

1

b 1 − b b

3 1 3

1 − a x − a , < x ≤ − ;

⎪

1 1

a a a

()

μ x =

3 1 3

⎨

b 1 − b

2

⎪ ⎪

1 − a x − b , −

3

< x ≤

3

;

3 3

a a

3 3

⎪ ⎪

1 − b

0

3

< x ≤ 1 .

a

⎩ 3

()

( )

y 0 ≤ 1

If function

y = a x + b

satisfies the conditions: ;

y − b / a < 0

, it is

3 3

1 1

b , and a is obtained from a normal equation of a
corresponding optimization problem. Membership functions look like

supposed that

1

1

1 ⎧

a x + 1 0 ≤ x ≤ − ;

⎪ ⎪
⎨

1

a

() ⎪ ⎪ ⎩

μ

x =

1

1

1

0 − < x ≤ 1

a

1

1

⎧

− a x , 0 ≤ x ≤ − ;

⎪

1

a

⎪

1

1 b

⎪

1 − < x ≤ −

3

;

⎪

a a

()

μ x =

1 3

⎨

2

b 1 − b

⎪

1 − a x − b , −

3

< x ≤

3

;

3 3

a a

⎪

3 3

⎪

1 − b

3

0 < x ≤ 1

⎪

a

⎩

3

() 1 ( )

y = a x + b

If function satisfies the conditions: y 0 ≤ ; y − b / a ≥ 0 , it is

1 1

3 3

( ) ( ) y − b / a = − a b / a + b = 0

a = a / b

b = 1

supposed that ; ; . Then

3 3 1 3 3 1 1 3 3

1