Intuitionistic Fuzzy Aggregation Techniques - Intuitionistic Fuzzy Aggregation and Clustering - page 124

(3) G κ α ,λ α ( α ) = ( κ α μ α ,λ α v α )

.

H κ α ,λ α (α) = (κ α μ α , v α + λ α π α )

(4) .

H κ α ,λ α (α) = (κ α μ α ,

(5) v α + λ α ( 1 − κ α μ α − v α )) .

(6) J

κ α ,λ α (α) = (μ α + κ α π α ,λ α

v

α )

.

J κ α ,λ α (α) = (μ α + κ α (

(7) 1 − μ α − λ α v

α ) ,λ α

v

α )

.

(8) P

κ α ,λ α (α) = (

max (κ α ,μ α ) , min (λ α , v

α ))

, where κ α + λ α ≤ 1.

(9) Q

κ α ,λ α (α) = (

min (κ α ,μ α ) , max (λ α , v

α ))

, where κ α + λ α ≤ 1.

Based on Definition 1.27, let

H ∗ , 0 F 0

κ

D 0
κ

G 0
κ

H 0
κ

( A ) = ( A ) = ( A ) = ( A ) =

κ x ,λ x (

A )

,λ ,λ ,λ ,λ x x x x x x x x

J ∗ , 0 J 0 P 0 Q 0 =

κ x ,λ x (

A ) =

κ x ,λ x (

A ) =

κ x ,λ x (

A ) =

κ x ,λ x (

A ) = A (1.303)

then we have the following theorem:

Theorem 1.43 (Xia and Xu 2010) Let α = (μ α , v α ) be an IFV, and n a positive

integer, taking κ α ,λ α ∈ [0 , 1], then

D n ( 1 )

κ α (α) = (μ α + κ α π α ,

v α + ( 1 − κ α ) π α ) .

n

1 − ( 1 − κ α − λ α )

F n

( 2 )

κ α ,λ α (α) =

μ α + κ α π α , v α

κ α + λ α

n

1 − ( 1 − κ α − λ α )

+ λ α π α , where κ α + λ α ≤ 1 .

κ α + λ α

κ α ,λ α (α) = κ

v α . G n

n n

α

( 3 )

α μ α ,λ

H n

n n

( 4 )

κ α ,λ α (α) =

κ

α μ α ,

v

α + (

1 − v

α )(

1 − ( 1 − λ α ) )

n − 1

t n − 1 − t

− μ α λ α

0 κ

− λ α ) .

( 1

α

t =

κ

v α ) 1

n

H ∗ , n

n

( 5 )

κ,λ (α) = α μ α ,

v α + ( 1 − − ( 1 − λ α )

n − 1

t n − 1 − t

− μ α κ α λ α

0 κ

( 1 − λ α ) .

α

t =

− μ α ) 1

n

( 6 ) J

κ α ,λ α (α) =

μ α + ( 1 − ( 1 − κ α )

n − 1

t n − 1 − t n

α

− v

α κ α

0 (

1 − κ α ) λ ,λ v .

α

α

t =