Methods of Expert Information Formalization Based on Complete Orthogonal Semantic Spaces - Expert Fuzzy Information Processing - page 77

c

⎧ 1

1 a ≤ x ≤ ;

⎪

2

⎪

⎛ c ⎞

⎪ ⎪

1

⎜ x − ⎟

c 3 c

2

()

⎜ ⎟

μ x = R ,

1

< x ≤

1

;

⎨ 1

c 2 2

⎜ ⎜ ⎟ ⎟

⎪

1

⎪ ⎝ ⎠

⎪ 3 c

0

1

< x ≤ b .

⎪

⎩ 2

c > c

2. If , then

1 2

⎧ ⎛ c ⎞ 2

1 a ≤ x ≤ ⎜ ⎝ c − ⎟ ⎠ ;

⎪

1

2

⎪

c

⎛ ⎞

⎪

− +

2

⎜ x c ⎟

⎪ c c

1

⎛ ⎞ ⎛ ⎞

2

()

⎜ ⎟

μ x = R , c −

2

< x ≤ c +

2

;

⎜ ⎝ ⎟ ⎠ ⎜ ⎝ ⎟ ⎠

⎨

1 1 1

⎜ ⎜

c

⎟ ⎟

2 2

⎪

2

⎪ ⎝ ⎠

⎪

c

⎛ ⎞

0 c +

2

< x ≤ b .

⎜ ⎝ ⎟ ⎠

⎪

1

2

⎩

If additional information on values of membership functions in the points of
universal set, which lie between typical intervals of the adjacent terms is available,
the updating of the form of membership functions is made in the same manner as
the previous method shows.
2.6 For mali zatio n of Li ng uistic Val ues of Pro perties on t he Basis of Direct Inquiry

2.6 Formalization of Linguistic Values of Properties on the
Basis of Direct Inquiry of Expert Groups about Regarding
Representatives

2.6 For mali zatio n of Li ng uistic Val ues of Pro perties on t he Basis of Direct Inquiry
Let k experts offer intervals of values, which are typical for each of m terms
from their point of view. It is possible to represent outcomes of their evaluations
in the form of the matrix
( ) ( ) ( )

⎛ x

1
11

, x

2
11

x

1
12

, x

2
12

... x

1
1

, x

2
1

⎞

⎜ ⎟

m m

( ) ( ) ( )

1
21

2
21

1
22

2
22

1
2

2
2

⎜ x , x x , x ... x , x ⎟

m m

A = .

⎜ ⎟

. . . .

⎜ ⎜ ⎟ ⎟

( ) ( ) ( )

x

1

, x

2

x

1

, x

2

... x

1

, x

2

⎝ ⎠ k 1 k 1 k 2 k 2 km km

Let