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In these methods connections between membership functions of terms
(presence of one maxima and fronts which are smoothly damping to zero are only
supposed for membership functions) are not described, moreover, there is no
algorithm of deriving of continuous membership functions based on their discrete
values. A model-building techniques of the semantic spaces developed by А.V.
Skofenko [77] is based on expert evaluations such as "approximately equal to
number
A
” or “lays approximately in the range between
A
and
B
”. In methods
[73—76] connections between membership functions of terms are not described
thus not allowing winning independence of quality of the constructed models from
skills of researchers.
In [78—79] A.N.Borisov and A.N.Averkin offered parametrical definition of
membership functions of the modified terms of semantic spaces on the basis of
membership functions of basic terms.
Considering the essential importance of formalization of the information
obtained while developing fuzzy models, building methods of COSS membership
functions will be considered in Chapter 2.
1.7 Formalization of Fuzzy Conclusions
Let
be semantic spaces corresponding to universal sets
X
,
X
,
...,
X
1
2
n
{}
l
=
1
m
U
,
U
,
...,
U
, accordingly, and terms
il
X
,
i
=
1
n
,
, with membership
1
2
n
{
()
}
μ
x
. Let
Y
be a semantic space with universal set
U
and terms
functions
il
{}
{
()
}
Y
, which have membership functions
.
The system of fuzzy reasonings can be of two types:
μ
x
l
,
21
— input information, and
Y
— output information, or
Y
is input information,
and
X
X
,
...,
X
n
,
21
— output information. System of approximate reasonings of
first type [80-81] or system of the reference fuzzy logic reasonings which reflect
expert experience could be presented as:
X
X
,
...,
X
n
⎧
X
X
X
X
X
X
if
and
and...and
or
and
and...and
~
1
1
11
21
n
1
12
21
n
1
A
:
;
⎪
or...or
X
and
X
and...and
X
,
then
Y
⎪
⎪
⎪
11
21
n
2
1
if
X
and
X
and...and
X
or
X
and
X
and...and
X
~
n
n
~
1
2
12
22
2
12
23
3
A
:
;
1
A
=
⎨
or...or
X
and
X
and...and
X
,
then
Y
13
23
n
2
2
⎪
..........
..........
..........
..........
..........
..........
..........
..
⎪
if
X
and
X
and...and
X
or
X
and
X
and...and
X
~
⎪
⎪
1
m
2
m
nm
1
m
2
m
−
1
nm
1
A
:
.
1
2
n
1
2
n
m
or...or
X
and
X
and...and
X
,
then
Y
⎩
1
m
−
1
2
m
nm
−
1
m
1
2
n
The second type of this system could be presented as:
