Intuitionistic Fuzzy Aggregation Techniques - Intuitionistic Fuzzy Aggregation and Clustering - page 154

α σ ( j ) is the j th largest of

m , F n
κ α σ ( j ) ,λ α σ ( j )

κ α σ ( j ) + λ α σ ( j ) ≤ = , ,...,

where 1, j 1 2

ω i F n

m

κ α i ,λ α i (α i ) (

i = 1 , 2 ,..., m ).

(3) GIFPHAG w ,ω (α 1 ,α 2 ,...,α m )

w 2 G n

α σ ( 2 ) ρ

w 1 G n

α σ ( 1 ) ρ
σ (

=

) ⊕

κ α σ ( 1 ) ,λ α σ ( 1 ) κ α σ ( 2 ) ,λ α σ ( 2 )

1

w m G n

α σ ( m ) ρ

1
ρ

⊕···⊕

κ α σ ( m ) ,λ α σ ( m )

α σ ( j ) is the j th largest of m

where G n
κ α σ ( j ) ,λ α σ ( j )

ω i G n

κ α i ,λ α i (α i ) (

i = 1 , 2 ,..., m ) .

(4) GIFPHAH w ,ω (α 1 ,α 2 ,...,α m )
w 1 H n

α σ ( 1 ) ρ

w 2 H n

α σ ( 2 ) ρ

⊕

κ σ ( 1 ) ,λ σ ( 1 ) κ σ ( 2 ) ,λ σ ( 2 )

w m H n

ρ

1
ρ

⊕···⊕

κ α σ ( m ) ,λ α σ ( m ) (α m )

α σ ( j ) is the j th largest of m

where H n
κ α σ ( j ) ,λ α σ ( j )

ω i H n

κ α i ,λ α i (α i ) (

i = 1 , 2 ,..., m ) .

(5) GIFPHAH ∗ , n
w ,ω (α 1 ,α 2 ,...,α m )

w 1 H ∗ , n

α σ ( 1 ) ρ

w 2 H ∗ , n

α σ ( 2 ) ρ

= ⊕

κ α σ ( 1 ) ,λ α σ ( 1 ) κ α σ ( 2 ) ,λ α σ ( 2 )

w m H ∗ , n

α σ ( m ) ρ

1
ρ

⊕···⊕

κ α σ ( m ) ,λ α σ ( m )

α σ ( j ) is the j th largest of m

where H ∗ , n
κ α σ ( j ) ,λ α σ ( j )

ω i H ∗ , n

κ α i ,λ α i (α i ) (

= , ,..., )

i 1 2 m .

(6) GIFPHAJ w ,ω (α 1 ,α 2 ,...,α m )

w 1 J n

α σ ( 1 ) ρ

w 2 J n

α σ ( 2 ) ρ

= ⊕

κ α σ ( 1 ) ,λ α σ ( 1 ) κ α σ ( 2 ) ,λ α σ ( 2 )

w m J n

α σ ( m ) ρ

1
ρ

⊕···⊕

κ α σ ( m ) ,λ α σ ( m )

α σ ( j ) is the j th largest of m

where J n
κ α σ ( j ) ,λ α σ ( j )

ω i J n

κ α i ,λ α i (α i ) (

i = 1 , 2 ,..., m ) .

(7) GIFPHAJ ∗ , n
w

,ω (α 1 ,α 2 ,...,α m )

w 1 J ∗ , n

α σ ( 1 ) ρ

w 2 J ∗ , n

α σ ( 2 ) ρ

= ⊕

κ α σ ( 1 ) ,λ α σ ( 1 ) κ α σ ( 2 ) ,λ α σ ( 2 )

w m J ∗ , n

α σ ( m ) ρ

1
ρ

⊕···⊕

κ α σ ( m ) ,λ α σ ( m )