Information Technology Reference
In-Depth Information
⎧
b
⎛
⎞
0
0
≤
x
≤
1
−
a
−
m
−
1
;
⎜
⎝
⎟
⎠
⎪
m
2
⎪
⎛
b
⎞
⎪
m
−
1
x
−
⎜
⎝
1
−
a
+
⎟
⎠
⎪
⎪
m
b
b
2
⎛
⎞
⎛
⎞
()
μ
x
1
+
,
1
−
a
−
m
−
1
<
x
≤
1
−
a
+
m
−
1
;
=
⎜
⎝
⎟
⎠
⎜
⎝
⎟
⎠
⎨
m
m
m
b
2
2
⎪
m
−
1
b
⎪
⎛
⎞
1
1
−
a
+
m
−
1
<
x
≤
1
.
⎜
⎝
⎟
⎠
⎪
m
2
⎪
⎪
⎩
Logic of requirements to fuzziness area imposed to construct COSS term-set
membership functions can be explained with the following simple example: when
a mean evaluation of knowledge (certificate, diploma etc.) is identified with one of
the accepted marks «2», «3», «4», «5», the mean evaluation which falls within an
interval (4; 4.5), for example, is identified with a mark «4», and the mean
evaluation which falls within an interval [4.5; 5] is identified with a mark «5». If
an expert has his/her own judgments concerning fuzziness areas between the
adjacent terms, then the building method is corrected and put into practice. If an
expert agrees with the interpretation of authors stated herein, or information is
processed by a person who does not possess expert experience, the information is
proposed for use without any modifications.
The described building of COSS membership functions is offered to be applied
not only in the conditions of availability of a posteriori information submitted to
processing. The expert can build COSS without such information at the moment
using the information which he/she enjoyed earlier owing to considerable
experience gained.
To estimate qualitative characteristics, verbal-numerical or numerical ordinal
scales can be used. The model-building techniques of COSS membership
functions with the use of these scales is invariable.
Example 2.1.
Model-building of COSS “quality of production”. A firm
manufactures production of the superior, first, second and third quality degrees.
Over a certain period, 523 production units of the superior quality, 1084
production units of the first quality, 857 production units of the second quality and
379 production units of the third quality are manufactured. Let us construct COSS
“quality of production” with terms
X
= {the third quality},
X
= {the second
2
quality},
X
= {the first quality},
X
: = {the superior quality}. Let us denote
4
()
()
μ
x
μ
x
X
, with
with
a membership function of
- a membership function of
1
2
()
()
μ
- a
membership function for
X
. Let us obtain relative frequencies for production
units of the first - third and superior qualities:
μ
x
x
X
, with
- a membership function of
X
, and with
3
4
2
a
=
0
133
a
=
0
301
a
=
0
382
,
,
,
1
2
3
a
=
0
184
, accordingly. Then
4
