Intuitionistic Fuzzy Clustering Algorithms - Intuitionistic Fuzzy Aggregation and Clustering - page 198

Fig. 2.1 Classification of the building materials A j ( j = 1 , 2 , 3 , 4 , 5 )

A 1 ={

x 1 , [ 0 . 70 , 0 . 75 ] , [ 0 . 10 , 0 . 15 ] , x 2 , [ 0 . 00 , 0 . 10 ] , [ 0 . 80 , 0 . 90 ] ,

x 3 , [ 0 . 15 , 0 . 20 ] , [ 0 . 60 , 0 . 65 ] , x 4 , [ 0 . 50 , 0 . 55 ] , [ 0 . 30 , 0 . 35 ] ,

x 5 , [ 0 . 10 , 0 . 15 ] , [ 0 . 50 , 0 . 60 ] , x 6 , [ 0 . 70 , 0 . 75 ] , [ 0 . 10 , 0 . 15 ]}

A 2 ={

x 1 , [

. , . ] , [ . , . ] ,

x 2 , [

. , . ] , [ . , . ] ,

0 40 0 45 0 30 0 35 0 60 0 65 0 20 0 30

x 3 , [ 0 . 80 , 1 . 00 ] , [ 0 . 00 , 0 . 00 ] , x 4 , [ 0 . 70 , 0 . 90 ] , [ 0 . 00 , 0 . 10 ] ,

x 5 , [ 0 . 70 , 0 . 75 ] , [ 0 . 10 , 0 . 20 ] , x 6 , [ 0 . 90 , 1 . 00 ] , [ 0 . 00 , 0 . 00 ]}

A 3 ={

x 1 , [ 0 . 20 , 0 . 30 ] , [ 0 . 40 , 0 . 45 ] , x 2 , [ 0 . 80 , 0 . 90 ] , [ 0 . 00 , 0 . 10 ] ,

x 3 , [ 0 . 10 , 0 . 20 ] , [ 0 . 70 , 0 . 80 ] , x 4 , [ 0 . 15 , 0 . 20 ] , [ 0 . 70 , 0 . 75 ] ,

x 5 , [ 0 . 00 , 0 . 10 ] , [ 0 . 80 , 0 . 90 ] , x 6 , [ 0 . 60 , 0 . 70 ] , [ 0 . 20 , 0 . 30 ]}

A 4 ={

x 1 , [ 0 . 60 , 0 . 65 ] , [ 0 . 30 , 0 . 35 ] , x 2 , [ 0 . 45 , 0 . 50 ] , [ 0 . 30 , 0 . 40 ] ,

x 3 , [ 0 . 20 , 0 . 25 ] , [ 0 . 65 , 0 . 70 ] , x 4 , [ 0 . 20 , 0 . 30 ] , [ 0 . 50 , 0 . 60 ] ,

x 5 , [ 0 . 00 , 0 . 10 ] , [ 0 . 75 , 0 . 80 ] , x 6 , [ 0 . 50 , 0 . 60 ] , [ 0 . 20 , 0 . 25 ]}

Here we can use Algorithm 2.4 to classify the enterprises A j (

j = 1 , 2 , 3 , 4 ) :

A j (

Step 1 In the first stage, each of the IVIFSs j = 1 , 2 , 3 , 4 ) is considered as a

unique cluster:

{ A 1 } , { A 2 } , { A 3 } , { A 4 }

Step 2 Compare each IVIFS A i with all the other three IVIFSs by using the
weighted Hamming distance ( 2.111 ):

d wH ( A 1 , A 2 ) = d wH ( A 2 , A 1 ) = d wH ( A 1 , A 3 ) = d wH ( A 3 , A 1 ) = 0 . 4600 , 0 . 4012

d wH ( A 1 , A 4 ) = d wH ( A 4 , A 1 ) = d wH ( A 2 , A 3 ) = d wH ( A 3 , A 2 ) =

0 . 2525 , 0 . 4237