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term-sets “low pressure”, “pressure close to 4”, “high pressure" of semantic space
“inlet steam pressure” is offered. However, a shortage of this formula is in lack of
symmetry attribute, i.e.
ρ ≠
[134] contains a formula of product analogy
degree determination based on COSS term-sets membership functions, which is
free from this shortage.
Let us consider
ρ
ab
ba
[
]
U
,=
as a range of parameter values. Based on his/her
experience, an expert selects
m
linguistic values of this parameter and specified
corresponding typical numerical values for each linguistic value. Typical values
can be specified by one number or by the entir
e i
nterval. Depending upon that,
membership functions of term-sets
B
()
(see §2.4) are membership
functions of unimodal or tolerance numbers from population
μ
x
,
l
=
1
m
l
constructed in
Λ
§2.1.
Let us identify
()
()
μ −
as a measure of information loss for values
a
and
b
within the limits of
l
-th term-set. Let us determine an analogy degree of
products with values
a
and
b
for the considered parameter by the formula
a
μ
b
l
l
m
()
()
.
∑
=
μ
ρ
From this formula it follows that if
a
and
b
belong to tolerance areas of one
function
a
−
μ
b
l
l
=
1
−
l
1
ab
2
[
()
()
]
ρ
=
1
μ
a
=
μ
b
=
1
, then
.
ab
l
l
a
and
b
belong to uncertainty areas of two adjacent functions
()
If
[
()
()
()
]
0
<
μ
a
<
1
<
μ
a
<
1
0
<
μ
b
<
1
0
<
μ
b
, or one of these values
belongs to tolerance area of one function, and another value - to uncertainty area
of the adjacent function, then
l
l
+
1
l
l
+
1
()
()
ρ
=
1
−
μ
a
−
μ
b
.
ab
l
l
(2.5)
The latter formula follows from characteristics of COSS term-set membership
functions
()
()
μ
a
+
μ
a
=
1
⎫
l
l
+
1
⎪
⎬
()
()
()
()
μ
b
+
μ
b
=
1
⇒
μ
a
−
μ
b
=
l
l
+
1
l
l
⎪
⎭
()
()
()
()
()
()
μ
b
−
μ
a
⇒
μ
a
−
μ
b
=
μ
a
−
μ
b
.
l
+
1
l
+
1
l
l
l
+
1
l
+
1
(2.6)
When comparing formulas (2.7) and (2.5), one can see that they are very similar,
though the first formula operates with the parameter values, the second one —
with values of their membership functions. The first formula includes a potency
(length) of a characteristic value range equal to (
B
-
A
), the second one includes a
potency of a range of membership functions values equal to 1. In other situations
0
ρ
=
.
ab
