Civil Engineering Reference
In-Depth Information
Tabl e 1
Memberships for
five factors with five
interviewees
Factors sample
1
2
3
4
5
1
0.10
0.10
0.6
0.10
0.10
2
0.20
0.15
0.5
0.05
0.10
3
0.10
0.10
0.7
0.05
0.05
4
0.10
0.20
0.5
0.10
0.10
5
0.25
0.10
0.4
0.15
0.10
Sum of memberships
0.75
0.65
2.7
0.45
0.45
w
0.15
0.13
0.54
0.09
0.09
n
i
=
1
m
ij
n
n
i
=
1
m
ij
n
0
.
75
5
=
=
∑
=
∑
It shows that
w
1
=
0
.
15
,...,
w
5
=
0
.
45
5
=
0
.
09.
the basic structure and characteristics of the information efficiently (
Wu 2000
).
However, many phenomena in the world, such as human language, thinking, and
decision making, all possess nonquantitative characteristics. Human behavior is
particularly difficult to quantize. It is about the principle of applying fuzzy scale and
categorization into human's interaction with the dynamic environment and to give
a more concrete description and solution toward complicated/vague phenomenon.
Therefore, to collect the information based on the fuzzy mode should be the first
step to take. What some information has embedded with uncertainty and ambiguity.
It is naturally for us to propose the fuzzy statistics, such as fuzzy mode and fuzzy
median, to fit the requirement of the status quo. In this and the next section we
demonstrate the definitions of fuzzy mode and fuzzy median generalized from the
traditional statistics.
How to decide the weights
, called fuzzy weights, becomes a primary work before
evaluating the specialized human capital. In this section we will demonstrate an
integrated design via appropriate questionnaires of field study to reach a common
agreement for weight of fuzzy factors for an object/event.
Here, the calculating process of entity fuzzy weight is presented:
Step 1: First, determine the factors A
A
K
for the specialized factors.
Step 2: Ask interviewees to give the importance of factors set with a membership
m
ij
=
A
1
,
A
2
,
j
1
m
ij
=
1
.Letm
ij
be the membership of importance of factor j for the
∑
=
interviewee.
Step 3: Calculate the fuzzy weight w
j
of A
j
by w
j
=
∑
i
1
m
ij
n
=
.
Example 2.1.
Suppose there are five interviewees to rank a certain event with five
factors for a discussion domain, Table
1
illustrates the result.
Distance among fuzzy data.
Once such a transformation has been selected, instead
of the original trapezoid data, we have a new value y = f(x). In the ideal situation,
this new quantity y is normally distributed. (In practice, a normal distribution for
y may be a good first approximation.) When selecting the transformation, we must
take into account that, due to the possibility of a rescaling, the numerical values of
the quantity x are not uniquely determined.
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