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However, not all models based on semantic spaces, possess the properties
ensuring successful solutions of practical problems. One such property is
completeness of model, which consists in a possibility of describing each element
of universal set in linguistic terms of this space [28. 35].
Let us consider a semantic space “steam pressure at inlet” when using a
high-pressure preheater, which was constructed in [35],
(){
[
]
}
XT
Where
A
— “low pressure”;
B
— “pressure close to 4”;
C
— “high input
pressure”.
Membership functions of the term-set of this semantic space are shown in
Fig. 1.6. b. If at the inlet of a high pressure preheater there is pressure equal 1.7,
this value cannot be described by any of linguistic values of the “steam pressure”
characteristic. So, we can conclude that the semantic space the membership
functions of which are shown in Fig. 1.6. b does not possess the completeness
property which means that each element of universal set can be described within
the scope of at least one of linguistic terms.
Another model which poorly describes evaluation processes is a semantic space
“system sensor failure probability” with terms of "low", "mean", "high"
probabilities. Membership functions of this space are shown in Fig. 1.6.c.
According to this model, the probability value equal to a is identified with all
terms included and consequently it does not have any meaning for further use.
So, a conclusion can be made that the semantic space which membership
functions are shown in Fig. 1.6.c, does not possess the property of concepts
discriminability which means that each element of universal set cannot be
described within the limits of more than two linguistic terms.
It is obvious that to solve practical problems, lack of completeness which
characterizes model of expert evaluations of object's properties and lack of
discriminability of concepts incorporated into this model, is the essential gap
which needs to be bridged.
=
A
,
B
,
C
,
U
=
1
6
,
1.5 Complete Orthogonal Semantic Spaces
Theoretical researches of semantic space properties aimed at improving the
adequacy of evaluations expert models and their usefulness for solution of
practical problems allow reasonable formulation of requirements to membership
functions
()
μ
x
;
and their term-sets [28].
l
=
1
m
l
{
()
}
U
≠
φ
1.
For each concept
X
the
exists, where
U
=
x
∈
U
:
μ
x
=
1
is a
l
l
l
point or a segment.
2.
Let
()
{
()
}
μ
x
U
=
x
∈
U
:
μ
x
=
1
, then
does not decrease at the left and does
l
l
l
not increase to the right of
U
.
l
()
μ
have no more than two points of discontinuity of the first kind.
4.
For every
x
3.
l
x
∈
U
