Information Technology Reference
In-Depth Information
Table 6.10
A matrix of the fuzzy relation describing values of logic function
F
for
arguments
Z
,
Z
,
Z
1
2
3
п
0
1
2
Z
(a)
F for argument
0
1
0,9
0,9
1
0,9
0,9
0,9
2
0
0
1
F
for argument
Z
(b)
0
1
0,7
0,7
1
0,7
0,7
0,7
2
0
0
1
Z
(c)
F
for argument
0
1
0,8
0,8
1
0,8
0,8
0,8
2
0
0
1
As a result of formalization of all conditions the relation is obtained with the
matrix of 27 lines (according to number of possible values of arguments) and 3
columns (according to number of function values). Matrix elements are values of
confidence degree saying that function
F
will accept any value depending on
values of arguments
Z
,
Z
,
Z
. For example, to obtain degree of confidence
saying that function
F
will take value 1 at
=
Z
, it is necessary
to take a minimum of an element of the matrix 6.10 (a) placed on the cross-section
of the first line and the second column, an element of a matrix 6.10 (b) placed on
the cross-section of the second line and the second column, and an element of a
matrix 6.10 (c) placed on the cross-section of the first line and the second column.
On completing all operations the fuzzy relation describing work of an
aggregation operator of information or functions
F
, is obtained. Elements of a
matrix of this relation are summarized in Table 6.11.
Discussing the obtained results with experts allowed obtaining the aggregation
operator of information in the form of function of three-value logic with three
variables. Results of work of this operator are summarized in Table 6.12.
Managerial instructions based on results of work of the operator are in the form
of the following logic rules (Table 6.14).
0
Z
=
0
,
Z
=
0
,
3
1
2
