Intuitionistic Fuzzy Clustering Algorithms - Intuitionistic Fuzzy Aggregation and Clustering - page 251

Table 2.16 The characteristics information of the cars
G 1 G 2 G 3 G 4 G 5 G 6

y 1 (0.3,0.5) (0.6,0.1) (0.4,0.3) (0.8,0.1) (0.1,0.6) (0.5,0.4)

y 2 (0.6,0.3) (0.5,0.2) (0.6,0.1) (0.7,0.1) (0.3,0.6) (0.4,0.3)

y 3 (0.4,0.4) (0.8,0.1) (0.5,0.1) (0.6,0.2) (0.4,0.5) (0.3,0.2)

y 4 (0.2,0.4) (0.4,0.1) (0.9,0.0) (0.8,0.1) (0.2.0.5) (0.7,0.1)

y 5 (0.5,0.2) (0.3,0.6) (0.6.0.3) (0.7,0.1) (0.6,0.2) (0.5,0.3)

-cutting
matrix. Replace '1' with '*' and delete all the '0' in the matrix before drawing
the vertical and horizontal line to the symbol of alternatives on the diagonal from
'*'. Corresponding to each '*', we have a type which contains two elements. Unit
the types together which have the common elements, and then we get the types
corresponding to the selected

Step 4 Choose the confidence level λ and construct the corresponding λ

λ . Update the values of λ before all the alternatives are

clustered into one type.

: Based on the idea of constructing the similarity
degree matrix, we balance the similarity degree of two alternatives mainly through
the membership degree of the corresponding IFV. We choose the confidence level

The principal to choose λ

λ
from the biggest one to the smallest one. When we encounter that two membership
degrees are equal, we firstly choose the one with the smaller non-membership degree.
If both of them are equal, they are clustered into the same type. After that, in terms of
the chosen

λ , we construct the corresponding λ -cutting matrix. With this principle,

the clustering results will be more detailed.

2.8.3 Illustrative Examples

Example 2.12 (Wang et al. 2011) An auto market wants to classify five different
cars y i ( into several kinds (Liang and Shi 2003). Each car has six

evaluation factors: (1) G 1 : Oil consumption; (2) G 2 : Coefficient of friction; (3) G 3 :
Price; (4) G 4 : Comfortable degree; (5) G 5 : Design; (6) G 6 : Safety coefficient. The
evaluation results of each car with respect to the factors G j

i = 1 , 2 , 3 , 4 , 5 )

( j = 1 , 2 ,..., 6 ) are

represented by the IFSs, shown as in Table 2.16 (Wang et al. 2011).
In the following, we utilize the intuitionistic fuzzy netting method to classify the
five cars, which involves the following steps (Wang et al. 2011):

Step 1 By Eq. ( 2.192 ), we calculate

6 6

1
6

1
6

μ 12 = 1 −

1 |

v 1 j − v 2 j |−

1 | π 1 j − π 2 j |

j = j =