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Table 2.18 The characteristics of the cars
G 1
G 2
G 3
G 4
G 5
G 6
y 1
(0.8,0.1)
(0.4,0.1)
(0.6,0.1)
(0.7,0.3)
(0.6,0.2)
(0.5,0.0)
y 2
(0.0,0.3)
(0.1,0.3)
(0.0,0.6)
(0.0,0.5)
(0.5,0.3)
(0.4,0.2)
y 3
(0.2,0.0)
(0.9,0.1)
(0.0,0.7)
(0.0,0.1)
(0.3,0.2)
(0.8,0.2)
y 4
(0.0,0.5)
(0.3,0.0)
(0.7,0.1)
(0.6,0.1)
(0.0.0.7)
(0.7,0.2)
y 5
(0.4,0.6)
(0.2,0.4)
(0.9.0.1)
(0.6,0.1)
(0.7,0.2)
(0.7,0.3)
y 6
(0.0,0.2)
(0.0,0.0)
(0.5.0.4)
(0.5,0.4)
(0.3,0.6)
(0.0,0.0)
y 7
(0.8,0.1)
(0.2,0.1)
(0.1.0.0)
(0.7,0.0)
(0.6,0.4)
(0.0,0.6)
y 8
(0.1,0.7)
(0.0,0.5)
(0.8.0.1)
(0.7,0.1)
(0.7,0.1)
(0.0,0.0)
y 9
(0.0,0.1)
(0.5,0.1)
(0.3.0.1)
(0.7,0.3)
(0.1,0.3)
(0.7,0.2)
y 10
(0.3,0.2)
(0.7,0.1)
(0.2.0.2)
(0.2,0.0)
(0.1,0.9)
(0.9,0.1)
similarity matrix contains. Considering the stated reasons above, it is not hard for
us to comprehend why the intuitionistic fuzzy netting method can get more detailed
types than Zhang et al. (2007).
Here we only make a comparison with that of Zhang et al. (2007), because that the
method in Zhang et al. (2007) is a representation of solving this class of problems,
some closely-related results can be found in Xu et al. (2008) and Cai et al. (2009).
In order to demonstrate the effectiveness of the proposed clustering algorithm, we
further conduct experiments with the simulated data through comparing these two
methods:
Example 2.13 (Wang et al. 2011) As we have explained above, the computational
complexity is mainly related with the computations of intuitionistic fuzzy similarity
matrix and intuitionistic fuzzy equivalent matrix. Next, we shall illustrate this with
simulated experiments. Below we first introduce the experimental tool, the exper-
imental data sets, and then make a comparison with other method (Zhang et al.
2007):
(1) Experimental tool. In the experiments, we use the netting algorithm imple-
mented by MATLAB. Note that if we let
X , then the netting
algorithm reduces to the traditional fuzzy netting algorithm. Therefore, we can use
this process to compare the performances of both the netting algorithm under intu-
itionistic fuzzy environment and the netting algorithm under fuzzy environment.
(2) Experimental data sets. The car data set contains the information of ten new
cars to be classified in an auto market. Let y i (
π(
x
) =
0 for any x
be the cars, each of
which is described by six attributes: (1) G 1 : Oil consumption; (2) G 2 : Coefficient
of friction; (3) G 3 : Price; (4) G 4 : Comfortable degree; (5) G 5 : Design; and (6) G 6 :
Safety coefficient, as in Example 2.12 (For convenience, here we do not consider
the weights of these attributes). The characteristics of the ten new cars under the six
attributes, generated at random by MATLAB, are represented by the IFSs, as shown
in Table 2.18 (Wang et al. 2011).
In order to express the validity of the netting method, we shall make a comparison
with Zhang et al. (2007)'s method:
i
=
1
,
2
,...,
10
)
 
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