Intuitionistic Fuzzy Clustering Algorithms - Intuitionistic Fuzzy Aggregation and Clustering - page 239

an intuitionistic fuzzy equivalent association matrix by transitive closure technique,
which needs lots of computational effort. In Zhao et al. (2012b)'s method, we get
the

-cutting matrix directly from the intuitionistic fuzzy association matrix.
Furthermore, Let m and n represent the amount of alternatives and attributes
respectively. Then the computational complexity of our method is O

λ

nm 2

( ) ,Xu

nm 2 et al. (2008)'s method is O represents the

transfer times until we get the equivalent matrix, and Pelekis et al. (2008)'s method
is O

(( 1 + k ) ) where k (usually, k ≥ 2 )

nm 2

( + jcm ) where c is the number of the clusters, j is the times of judgment if

U j + 1

U j F >ε

is valid.
In summary, Xu et al. (2008)'s method and Pelekis et al. (2008)'s method have
relatively high computational complexity, which indeed motivates the intuitionistic
fuzzy Boole clustering method given by Zhao et al. (2012b).
Furthermore, from Examples 2.8 and 2.9, we can see that the clustering results
have much to do with the threshold

−

λ , the smaller the confidence level λ is, the more

detailed the clustering will be.
Either in Example 2.8 or in Example 2.9, we all use the association coefficient
Eq. ( 2.159 ) but not Eq. ( 2.157 ), the reason is that Eq. ( 2.157 ) cannot guarantee the
necessity in the condition (2) of Definition 2.31 and omits the hesitation degree,
which may lead to the incorrect results. The following example shows these ideas:

Example 2.10 (Zhao et al. 2012b) Suppose that the military experts evaluate the
performance of another group of combat aircrafts y i ( i = 1 , 2 ,..., 9 ) 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 6 , 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 , 0 . 8 , 0 . 1 , G 2 , 0 . 5 , 0 . 2 , G 3 , 0 . 7 , 0 . 1 ,
G 4 , 0 . 7 , 0 . 1 , G 5 , 0 . 7 , 0 . 2 , G 6 , 0 . 8 , 0 . 1 , G 7 , 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 ,

. , . , G 2 , . , . , G 3 , . , . ,

0 5 0 2 0 7 0 2 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 }