Information Technology Reference
In-Depth Information
a
−
x
a
−
x
⎧
1
−
1
,
0
<
1
≤
1
a
>
0
⎪
L
a
a
⎪
⎪
L
L
x
−
a
x
−
a
()
1
−
1
,
0
<
1
≤
1
a
>
0
μ
x
=
⎨
~
R
a
a
A
⎪
R
R
1
x
=
a
;
⎪
1
⎪
0
x
<
a
−
a
or
x
>
a
+
a
.
⎩
1
L
1
R
1.4 Linguistic Variables and Semantic Spaces
One of the basic concepts of the fuzzy set theory is the concept of a fuzzy variable
[4].
A triple
X
~
{
}
,,
is referred to as a fuzzy variable, where
X
- the name of the variable;
U
— area
of its definition (universal set);
~
— the fuzzy set of universal set which
describes possible values of the fuzzy variable.
On the basis of concept of a fuzzy variable the concept of a linguistic variable
is introduced.
A quintuple
A
{
()
}
X
,
T
X
,
U
,
V
,
S
,
()
{
}
is referred to as a linguistic variable, where
— a term-set of a
variable
X
, i.e. set of terms or titles of linguistic values of the variable (each of
them is a fuzzy variable with values from universal set
U
);
T
X
=
X
,
i
=
1
m
i
V
- Syntactic rule generating titles of values of the linguistic variable
X
;
S
- Semantic rule which puts a fuzzy subset of universal set
U
in conformity
to each fuzzy variable with a title from
()
.
T
X
Terms
X
are concepts which form a linguistic variable [28]. Membership
functions of fuzzy sets
~
describing possible values of fuzzy variables with titles
X
are traditionally referred to as membership functions of concepts
X
, or
membership functions of terms
X
. According to one of psycholinguistics
principles, namely, to a principle linguistic complementarity [45], membership
functions of the same concepts used by different people, do not necessarily
coincide.
i
