Methods of Expert Information Formalization Based on Complete Orthogonal Semantic Spaces - Expert Fuzzy Information Processing - page 79

⎧

2
1

1 a ≤ x ≤ x ;

⎪ ⎪
⎨

⎛ x − x

2
1

⎞

() ⎪ ⎪

⎜ ⎜
⎝

⎟ ⎟
⎠

2
1

1
2

μ x = L , x < x ≤ x ;

1

x

1
2

− x

2
1

1
2

0 x < x ≤ b ;

⎩

2
1

⎧ 0 a ≤ x ≤ x ;

⎪

⎛

1
2

⎞

x − x

⎪

⎜ ⎜
⎝

⎟ ⎟
⎠

2
1

1
2

L , x < x ≤ x ;

1
2

2
1

⎪ ⎪

x − x

()

μ x =

1
2

2
2

1 x < x ≤ x ;

⎨ 2

⎪

⎛

2
2

⎞

x − x

⎜ ⎜
⎝

⎟ ⎟
⎠

2
2

1
3

⎪ R , x < x ≤ x ;

x

1
3

− x

2
2 ⎪

⎪

1
3

0 x < x ≤ b ;

⎩

……………………………………………………

⎧

2

0 a ≤ x ≤ x ;

m − 2

⎪

⎛

1

⎞

x − x

⎪

⎜ ⎜
⎝

m − 1

⎟ ⎟
⎠

2 1

R , x < x ≤ x ;

m − 2 m − 1

1 2

⎪ ⎪

x − x

m − 1 m − 2

()

μ x =

1 2

1 x < x ≤ x ;

⎨ m − 1 m − 1 m − 1

⎪

⎛ −

2

⎞

x x

⎪ L

⎜ ⎜
⎝

m − 1

⎟ ⎟
⎠

, x

2

< x ≤ x

1

;

m − 1 m

1 2

x − x

⎪ m m − 1

⎪

1

0 x < x ≤ b ;

⎩

m

⎧ 0 a ≤ x ≤ x

2

;

m − 1

⎪ ⎪
⎨

⎛ x

1

− x ⎞

() ⎪ ⎪

⎜ ⎜
⎝

⎟ ⎟
⎠

2 1

μ x = L

m

, x < x ≤ x ; .

m m − 1 m

1 2

x − x

m m − 1

1 x

1

< x ≤ b

⎩

m

()

With odd m two last membership functions

()

R interchange.
If obtaining of an additional information on values of membership functions in
the points of universal set, which lie between typical intervals of the adjacent
terms is possible, the form of membership functions of terms is updated.

,

L x

Example 2.5. Model-building of COSS “pressure at the high-pressure preheater
inlet”. Let us construct COSS “pressure at the high-pressure preheater inlet” with
terms “very low pressure”, “low pressure”, “normal pressure”, "high pressure".
Three experts offer their typical values for each of terms. The first expert:
{1.1}, {1.7}, {4}, {6.7}. The second expert: [1.1; 1.3], {1.7}, {4}, [6.6; 6.7]. The
third expert: {1.1}, [1.6; 1.7], {4}, {6.7}. Based on intersections of typical values
corresponding to each of terms, we obtain COSS which membership functions are
shown in Fig. 2.6.