Intuitionistic Fuzzy Clustering Algorithms - Intuitionistic Fuzzy Aggregation and Clustering - page 176

. <λ ≤ .

(3) When 0 78 0 92, we have

⎛
⎝

⎞
⎠

1
2

1
2

1
2

1
2

1

1
2

1
2

1
2

1
2

1

1
2

1
2

1
2

1
2

Z ∗ =

1

λ

1
2

1
2

1
2

1
2

1

1
2

1
2

1
2

1
2

1

(4) When 0 . 92 <λ ≤ 1, we have

⎛
⎝

⎞
⎠

100 1

2 0
0100 1
2
00100
1
2 0010
0

Z ∗ =

λ

1
2 001

Step 4 According to λ Z ∗ and Definition 2.8, we make the following discussions:
(1) If 0 ≤ λ ≤ 0 . 71, then the cars y i ( i = 1 , 2 ,..., 5 ) are classified into one type:

{ y 1 , y 2 , y 3 , y 4 , y 5 }

(2) If 0 . 71 <λ ≤ 0 . 78, then the cars y i ( i = 1 , 2 ,..., 5 ) are classified into three

types:

{ y 1 , y 2 , y 3 } , { y 4 } , { y 5 }

. <λ ≤ ( = , ,..., )

(3) If 0 78 1, then the cars y i i 1 2 5 are classified into five

types:

{ y 1 } , { y 2 } , { y 3 } , { y 4 } , { y 5 }

From the above analysis, it can be seen that the clustering of the alternatives
(or IFSs) is closely related to the predefined confidence level λ . How to select the

confidence level is an interesting issue. We suggest the interested readers should

refer to the literature (Wang 1983).

λ