Methods of Expert Information Formalization Based on Complete Orthogonal Semantic Spaces - Expert Fuzzy Information Processing - page 76

⎧ ⎛ 3 c ⎞

0 a ≤ x ≤ b − c −

m − 1

;

⎜ ⎝ ⎟ ⎠

⎪

m

2

⎪

⎛ c ⎞

⎪

m − 1

⎜ b − c − − x ⎟

3 c c

⎪

m

⎛ ⎞ ⎛ ⎞

2

⎜ ⎟

R , b − c −

m − 1

< x ≤ b − c −

m − 1

;

⎜ ⎝ ⎟ ⎠ ⎜ ⎝ ⎟ ⎠

⎪

m m

⎜ ⎜

c

⎟ ⎟

2 2

⎪ ⎪

m − 1

⎝ ⎠

()

μ x =

⎨

m − 1

⎛ c ⎞

⎪

m − 1

x − b + c +

⎜ ⎟

c c

⎛ ⎞ ⎛ ⎞

m

⎪ 2

⎜ ⎟

L , b − c −

m − 1

< x ≤ b − c +

m − 1

;

⎜ ⎝ ⎟ ⎠ ⎜ ⎝ ⎟ ⎠

⎪

m m

c 2 2

⎜ ⎜ ⎟ ⎟

m − 1

⎪

⎝ ⎠

⎪

c

⎛ ⎞

⎪

0 b − c +

m − 1

< x ≤ b .

⎜ ⎝ ⎟ ⎠

⎪

m

2

⎩

()

()

μ x

μ x

Similarly to membership functions , for term

X are

l = 2 m − 2

m 1 − l

constructed.

With even number of terms:

c ≤ c

1. If , then

1 2

c

⎧

1 a ≤ x ≤

1

;

⎪

2

⎪

c

⎛ ⎞

⎪ ⎪

1

⎜ x − ⎟

c 3 c

2

()

⎜ ⎟

μ x = L ,

1

< x ≤

1

;

⎨ 1

c 2 2

⎜ ⎜ ⎟ ⎟

⎪

1

⎪ ⎝ ⎠

⎪ 3 c

0

1

< x ≤ b .

⎪

⎩ 2

c > c

2. If , then

1 2

⎧ c

⎛ ⎞

1 a ≤ x ≤ c −

2

;

⎜ ⎝ ⎟ ⎠

⎪

1

2

⎪

c

⎛ ⎞

⎪

x c

2

⎜ − + ⎟

⎪ c c

1

⎛ ⎞ ⎛ ⎞

2

()

⎜ ⎟

μ x = L , c −

2

< x ≤ c +

2

;

⎜ ⎝ ⎟ ⎠ ⎜ ⎝ ⎟ ⎠

⎨ 1 1 1

⎜ ⎜

c

⎟ ⎟

2 2

⎪

2

⎪ ⎝ ⎠

⎪

⎛ c ⎞

2

0 ⎜ ⎝ c + ⎟ ⎠ < x ≤ b .

⎪ 1

2

⎩

With odd number of terms:

c ≤ c

1. If , then

1 2