Intuitionistic Fuzzy Clustering Algorithms - Intuitionistic Fuzzy Aggregation and Clustering - page 237

Example 2.9 (Zhao et al. 2012b) Below we first introduce the experimental data
sets, and then make a comparison among these methods:
Experimental data sets : Suppose that the military experts evaluate the perfor-
mance of another group of combat aircrafts y i ( i = 1 , 2 ,..., 10 ) according to the

attributes G j ( j = 1 , 2 ,..., 7 ) , and give the data as:

y 1 ={ G 1 , 0 . 5 , 0 . 3 , G 2 , 0 . 6 , 0 . 3 , G 3 , 0 . 4 , 0 . 3 ,

G 4 , 0 . 8 , 0 . 1 , G 5 , 0 . 7 , 0 . 2 , G 6 , 0 . 5 , 0 . 2 , G 7 , 0 . 4 , 0 . 3 }

y 2 ={ G 1 , 0 . 6 , 0 . 2 , G 2 , 0 . 5 , 0 . 3 , G 3 , 0 . 5 , 0 . 2 ,

G 4 , 0 . 6 , 0 . 2 , G 5 , 0 . 6 , 0 . 3 , G 6 , 0 . 6 , 0 . 3 , G 7 , 0 . 5 , 0 . 2 }

y 3 ={ G 1 , 0 . 7 , 0 . 1 , G 2 , 0 . 6 , 0 . 3 , G 3 , 0 . 7 , 0 . 2 ,

G 4 , 0 . 5 , 0 . 3 , G 5 , 0 . 5 , 0 . 2 , G , 0 . 5 , 0 . 2 , G 7 , 0 . 6 , 0 . 3 }

y 4 ={ G 1 , 0 . 4 , 0 . 3 , G 2 , 0 . 7 , 0 . 2 , G 3 , 0 . 5 , 0 . 3 ,

G 4 , 0 . 6 , 0 . 2 , G 5 , 0 . 7 , 0 . 1 , G 6 , 0 . 4 , 0 . 3 , G 7 , 0 . 7 , 0 . 2 }

y 5 ={ G 1 , 0 . 6 , 0 . 2 , G 2 , 0 . 6 , 0 . 3 , G 3 , 0 . 6 , 0 . 2 ,

G 4 , 0 . 5 , 0 . 3 , G 5 , 0 . 8 , 0 . 1 , G 6 , 0 . 6 , 0 . 1 , G 7 , 0 . 6 , 0 . 1 }

y 6 ={ G 1 ,

. , . ,

G 2 ,

. , . ,

G 3 ,

. , . ,

0 8 0 1 0 5 0 2 0 7 0 1

G 4 ,

. , . ,

G 5 ,

. , . ,

G 6 ,

. , . ,

G 7 ,

. , . }

0 7 0 1 0 7 0 2 0 8 0 1 0 7 0 2

y 7 ={ G 1 , 0 . 7 , 0 . 2 , G 2 , 0 . 6 , 0 . 3 , G 3 , 0 . 8 , 0 . 1 ,

G 4 , 0 . 8 , 0 . 1 , G 5 , 0 . 6 , 0 . 3 , G 6 , 0 . 5 , 0 . 4 , G 7 , 0 . 8 , 0 . 1 }

y 8 ={ G 1 , 0 . 5 , 0 . 2 , G 2 , 0 . 7 , 0 . 2 , G 3 , 0 . 7 , 0 . 2 ,

G 4 , 0 . 6 , 0 . 2 , G 5 , 0 . 5 , 0 . 3 , G 6 , 0 . 7 , 0 . 1 , G 7 , 0 . 6 , 0 . 2 }

y 9 ={ G 1 , 0 . 6 , 0 . 2 , G 2 , 0 . 5 , 0 . 3 , G 3 , 0 . 6 , 0 . 3 ,

G 4 , 0 . 5 , 0 . 2 , G 5 , 0 . 8 , 0 . 1 , G 6 , 0 . 8 , 0 . 1 , G 7 , 0 . 5 , 0 . 2 }

y 10 ={ G 1 , 0 . 9 , 0 . 0 , G 2 , 0 . 9 , 0 . 1 , G 3 , 0 . 8 , 0 . 1 ,

G 4 , 0 . 7 , 0 . 2 , G 5 , 0 . 5 , 0 . 15 , G 6 , 0 . 3 , 0 . 65 , G 7 , 0 . 15 , 0 . 75 }

Comparison results among these methods are listed in Table 2.14 (Zhao et al. 2012b).
Again we can see from Table 2.14 that Zhao et al. (2012b)'s method has the
same clustering results with those of Xu et al. (2008)'s method, and Pelekis et al.
(2008)'s method can make more detailed clustering results. It is worthy of pointing
out that the clustering results of Zhao et al. (2012b)'s method are exactly the same
with those of Xu et al. (2008)'s method, but Zhao et al. (2012b)'s method does not
need to use the transitive closure technique to calculate the equivalent matrix of the
association matrix, and thus requires much less computational effort than Xu et al.
(2008)'s method. Let's examine into the computing process of the two methods:
whether in Xu et al. (2008)'s method or Zhao et al. (2012b)'s method, the clustering
processes are all based on

λ λ

-cutting matrix,
Xu et al. (2008) first transformed the intuitionistic fuzzy association matrix into

-cutting matrix. Before getting the