Intuitionistic Fuzzy Aggregation Techniques - Intuitionistic Fuzzy Aggregation and Clustering - page 30

Table 1.2 Intuitionistic
fuzzy decision matrix B ( 1 )

y 1 y 2 y 3 y 4

G 1 (0.5,0.4,0.1) (0.4,0.5,0.1) (0.8,0.2,0.0) (0.5,0.3,0.2)

G 2 (0.5,0.5,0.0) (0.6,0.4,0.0) (0.7,0.3,0.0) (0.6,0.2,0.2)

G 3 (0.7,0.3,0.0) (0.2,0.5,0.3) (0.4,0.6,0.0) (0.5,0.1,0.4)

G 4 (0.3,0.6,0.1) (0.5,0.3,0.2) (0.5,0.2,0.3) (0.8,0.1,0.1)

Table 1.3 Intuitionistic
fuzzy decision matrix B ( 2 )

y 1 y 2 y 3 y 4

G 1 (0.6,0.3,0.1) (0.3,0.4,0.3) (0.9,0.1,0.0) (0.6,0.2,0.2)

G 2 (0.3,0.5,0.2) (0.5,0.3,0.2) (0.5,0.2,0.3) (0.7,0.3,0.0)

G 3 (0.5,0.2,0.3) (0.2,0.6,0.2) (0.4,0.4,0.2) (0.4,0.2,0.4)

G 4 (0.4,0.5,0.1) (0.6,0.4,0.0) (0.4,0.6,0.0) (0.7,0.1,0.2)

Table 1.4 Intuitionistic
fuzzy decision matrix B ( 3 )

y 1 y 2 y 3 y 4

G 1 (0.4,0.5,0.1) (0.4,0.6,0.0) (0.7,0.3,0.0) (0.7,0.2,0.1)

G 2 (0.5,0.4,0.1) (0.7,0.3,0.0) (0.6,0.4,0.0) (0.5,0.3,0.2)

G 3 (0.6,0.2,0.2) (0.3,0.5,0.2) (0.3,0.5,0.2) (0.9,0.1,0.0)

G 4 (0.3,0.5,0.2) (0.5,0.5,0.0) (0.6,0.2,0.2) (0.6,0.4,0.0)

Table 1.5 Intuitionistic
fuzzy decision matrix R ( 1 )

y 1 y 2 y 3 y 4

G 1 (0.4,0.5,0.1) (0.5,0.4,0.1) (0.2,0.8,0.0) (0.3,0.5,0.2)

G 2 (0.5,0.5,0.0) (0.6,0.4,0.0) (0.7,0.3,0.0) (0.6,0.2,0.2)

G 3 (0.7,0.3,0.0) (0.2,0.5,0.3) (0.4,0.6,0.0) (0.5,0.1,0.4)

G 4 (0.3,0.6,0.1) (0.5,0.3,0.2) (0.5,0.2,0.3) (0.8,0.1,0.1)

b ( k )
ij

r ( k )
ij

Eq. ( 1.50 ), then B ( k ) = ( are transformed into R ( k ) = (

) 4 × 4 ( k = 1 , 2 , 3 ) ) 4 × 4

( k (see Tables 1.5 , 1.6 , 1.7 ) (Xu 2011).

Considering that the weights of the experts are known, here, we utilize Approach
1.1 to select the software packages:

= 1 , 2 , 3 )

ξ ( k )
ij

Step 1 Utilize Eqs. ( 1.51 )-( 1.54 ) to calculate the weights ( i , j = 1 , 2 , 3 , 4 ;

associated with the attribute values r ( k )
ij

k = 1 , 2 , 3 ) ( i , j = 1 , 2 , 3 , 4 ; k = 1 , 2 , 3 ) ,

k = (ξ ( k ) which are contained in the matrices ) 4 × 4 ( k = 1 , 2 , 3 ) respectively:

ij

Table 1.6 Intuitionistic
fuzzy decision matrix R ( 2 )

y 1 y 2 y 3 y 4

G 1 (0.3,0.6,0.1) (0.4,0.3,0.3) (0.1,0.9,0.0) (0.2,0.6,0.2)

G 2 (0.3,0.5,0.2) (0.5,0.3,0.2) (0.5,0.2,0.3) (0.7,0.3,0.0)

G 3 (0.5,0.2,0.3) (0.2,0.6,0.2) (0.4,0.4,0.2) (0.4,0.2,0.4)

G 4 (0.4,0.5,0.1) (0.6,0.4,0.0) (0.4,0.3,0.3) (0.7,0.1,0.2)