Intuitionistic Fuzzy Aggregation Techniques - Intuitionistic Fuzzy Aggregation and Clustering - page 56

⎛

⎛ ⎞

1
2

⎝

n

⎝ 1

− μ α j )

⎠

1
n ( n − 1 )

= 1 − 1 − − ( 1 − μ α i )( 1 ,

i , j = 1
i

= j

⎛
⎝

⎞
⎠

1
2

n

1

j

1
n ( n − 1 )

1 − − v

i v

,

α α

i , j = 1

i = j

⎛ ⎞

1
2

n

⎝ 1

− μ α j )

⎠

1
n ( n − 1 )

1 − − ( 1 − μ α i )( 1

i , j = 1
i = j

2 ⎞
⎠

⎛ ⎞

1

n

⎝ 1

α j

⎠

1
n ( n − 1 )

− 1 − − v

α i v

(1.140)

i , j = 1

i = j

which is called an intuitionistic fuzzy interrelated square geometric mean
(IFISGM).

1.4.3 The Weighted Intuitionistic Fuzzy Geometric Bonferroni
Mean and Its Application in Multi-Attribute Decision Making

For a multi-attribute decision making problem. Let Y , G and w be defined as in
Sect. 1.2.4 . The performance of the alternative y i with respect to the attribute G j is
measured by an IFV b ij = (μ ij , v ij ,π ij ) , such that μ ij ∈[ 0 , 1 ] , v ij ∈[ 0 , 1 ] ,μ ij + v ij +

π ij = 1. All b ij ( i = 1 , 2 ,..., n ; j = 1 , 2 ,..., m ) are contained in an intuitionistic

b ij ) n × m .
To get the priority of the alternatives, we should aggregate the performance of
each alternative, however, it is noted that the IFGBMdoesn't consider the importance
of the aggregated arguments, but in many practical problems, especially in multi-
attribute decision making, the weight vector of the attributes is an important part
in the aggregation, to avoid this issue, Xia et al. (2012a) introduced the following
definition:

= (

fuzzy decision matrix B

T be the weight vector

Definition 1.9 (Xia et al. 2012a) Let w = ( w 1 , w 2 ,..., w n )

of the IFVs α i ( i = 1 , 2 ,..., n ) , where w i indicates the importance degree of α i ,

, i = 1 w i

satisfying w i > 0 ( i = 1 , 2 ,..., n ) = 1. If