Intuitionistic Fuzzy Aggregation Techniques - Intuitionistic Fuzzy Aggregation and Clustering - page 145

T , n

= ( / , / ,..., / ) = ρ =

(5) If w 1 m 1 m 1 m 0 and 1, then the GIFPWA operators

reduce to the following:

1
n (α 1 ⊕ α 2 ⊕···⊕ α m )

IFA w (α 1 ,α 2 ,...,α m ) = (1.394)

which is called an intuitionistic fuzzy average operator (Xu 2007).

T , n

(6) If w = ( 1 / m , 1 / m ,..., 1 / m ) = 0 and ρ → 0, then the GIFPWA operators

reduces to the following:

n

IFGM w (α 1 ,α 2 ,...,α m ) = (α 1 ⊗ α 2 ⊗···⊗ α m ) (1.395)

which is the IFGM (Xu and Yager 2006).

Definition 1.29 (Xia and Xu 2010) If
(1) GIFPOWAD w (α 1 ,α 2 ,...,α m )

w 1 D n

α σ ( 1 ) ρ

w 2 D n

α σ ( 2 ) ρ

= ⊕ ⊕···

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

w m D n

α σ ( m ) ρ

1
ρ

⊕

κ α σ ( m ) ,λ α σ ( m )

α σ ( j ) is the j th largest of D n

where D n
κ α σ ( j ) ,λ α σ ( j )

κ α i ,λ α i (α i ) (

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

GIFPOWAF w (α 1 ,α 2 ,...,α m ) (2)

w 1 F n

α σ ( 1 ) ρ

w 2 F n

α σ ( 2 ) ρ

= ⊕ ⊕···

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

w m F 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 , F n
κ α σ ( j ) ,λ α σ ( j )

where κ α σ ( j ) + λ α σ ( j ) ≤ 1, j = 1 , 2 ,...,

F n

κ α i ,λ α i (α i )

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

GIFPOWAG w (α 1 ,α 2 ,...,α m )

(3)

w 1 G n

α σ ( 1 ) ρ

w 2 G n

α σ ( 2 ) ρ

= ⊕ ⊕···

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

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 G n

where G n
κ α σ ( j ) ,λ α σ ( j ) κ α i ,λ α i (α i ) (

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