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()
()
()
()
()
μ
3
3
B
=
0
3
2
μ
3
3
C
=
0
7
μ
4
3
A
=
0
4
4
μ
C
=
0
μ
A
=
0
;
;
;
;
()
()
()
()
4
3
4
3
μ
B
=
0
2
μ
4
4
A
=
0
μ
C
=
0
2
4
4
μ
C
=
0
.
To define the "A", “B", "C" values of membership to fuzzy set “the software
which is thought proper for purchase” with membership function, the following
rule was applied [15]:
;
;
;
[
]
[
]
()
()
()
()
()
() ()
()
1
1
2
3
3
3
4
4
1
1
2
3
3
3
4
3
min
μ
x
,
μ
x
,
μ
x
,
μ
x
;
min
μ
x
,
μ
x
,
μ
x
,
μ
x
;
[
]
[
]
()
()
()
()
()
() ()
()
1
1
2
3
3
2
4
4
1
1
2
2
3
3
4
4
min
μ
x
,
μ
x
,
μ
x
,
μ
x
;
min
μ
x
,
μ
x
,
μ
x
,
μ
x
;
()
μ
x
=
max
[
]
[
]
()
()
()
()
()
() ()
()
1
2
2
3
3
3
4
4
1
2
2
3
3
3
4
3
min
μ
x
,
μ
x
,
μ
x
,
μ
x
;
min
μ
x
,
μ
x
,
μ
x
,
μ
x
;
[
]
[
]
()
()
()
()
()
() ()
()
min
μ
1
2
x
,
μ
2
3
x
,
μ
3
2
x
,
μ
4
4
x
;
min
μ
1
2
x
,
μ
2
2
x
,
μ
3
3
x
,
μ
4
4
x
.
The results of computations are as follows:
()
()
()
μ
A
=
0
6
μ
B
=
0
μ
C
=
0
54
;
;
.
On the basis of the obtained results the decision on software “B” purchase is
made.
Example 2.8. Definition of analogy degree for products. While solving
engineering problems, it is often necessary to define analogy degree of a product
by some parameters a and b [35]
a
b
ρ
=
1
,
ab
B
A
(2.4)
[
]
where
A , is a range of parameter values.
Advantage of this formula is simplicity of calculations, and its disadvantage is
that analogy degree only depends on a difference of parameter values and does not
depend on location of these values over the whole area
B
[
]
A , .
This disadvantage is the reason of the fact that outcomes obtained with this
formula do not always match expert experience. The matter is that a qualified
expert selects some base values of parameter within a set of parameters and makes
comparison of products on the basis of selected values. For example, an expert
selects low, mean and high values, and defines analogy of products depending on
what linguistic values of parameter its numerical values belong to [35] gives the
example of definition of analogy degree of products referred as “high pressure
preheater” by the parameter “inlet steam pressure”. The parameter has a definition
range [1.1, 6.7]. In this example analogy degrees of products with values (1.1 and
1.5) and (6.1 and 6.6) are defined. The above formula provides analogy degree
0.93 for first pair of products and 0.91 for second pair. In [35] it is stated that these
outcomes do not match the experience of experts. Moreover, based on the analysis
of expert experience in designing similar products, products of the first pair are
much less similar to each other than products of the second pair. In [35] a new
formula to define product analogy degree based on membership functions of
B
 
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