Intuitionistic Fuzzy Aggregation Techniques - Intuitionistic Fuzzy Aggregation and Clustering - page 77

α − and α + be given by Eqs. ( 1.35 ) and ( 1.36 ), then

Theorem 1.26 Let

α − ≤ GIFWBGM p , q (α 1 ,α 2 ,...,α n ) ≤ α +

(1.186)

In what follows, we apply the aggregation operators proposed in Sects. 1.5.2 and
1.5.3 to multi-attribute decision making with intuitionistic fuzzy information:
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 = ( t ij , f ij ,π ij ) , and all b ij ( i = 1 , 2 ,..., n ;

j = 1 , 2 ,..., m ) are contained in the intuitionistic fuzzy decision matrix

b ij ) n × m . Then an approach is given for multi-criteria decision making under
intuitionistic fuzzy environments (Xia et al. 2012b):

B = (

Step 1 Transform the matrix B = ( b ij ) m × n into the normalized intuitionistic fuzzy

decision matrix R = ( r ij ) n × m by Xu and Hu (2010)'s method, where

b ij ,

for benefit attribute G j

r ij = (μ ij , v ij ,π ij ) = ,

b ij ,

for cost attribute G j

i = 1 , 2 ,..., m ; j = 1 , 2 ,..., n (1.187)

where b ij is the complement of b ij , such that b ij = (

f ij , t ij ,π ij ) .

of the i th line,
and get the overall performance value r i corresponding to the alternative y i by the
GIFWBM or the GIFWBGM:

Step 2 Aggregate all the performance values r ij ( j = 1 , 2 ,..., n )

GIFWBM p , q , r
w

r i = (μ i , v i ,π i ) = ( r i 1 , r i 2 ,..., r in )

r il w j w k w l r ij

1
p + q + r

n
⊕

r q

= ⊗

ik ⊗

(1.188)

j , k , l = 1

or

GIFWBGM p , q , r
w

r i = (μ i , v i ,π i ) = ( r i 1 , r i 2 ,..., r in )

rr il w j w k w l

pr ij ⊕

1

n
⊗
j , k , l = 1

= qr ik ⊕ (1.189)

p + q + r

where p 0.

Step 3 Rank the overall performance values r i

, q , r >

( = , ,..., )

according to
Xu and Yager (2006)'s ranking method and obtain the priority of the alternatives
y i

i 1 2 m

( i = 1 , 2 ,..., m ) according to r i ( i = 1 , 2 ,..., m ) .

Next, we give an example to illustrate the proposed approach:

Example 1.6 (Wu and Chen 2011) We know that human resource management is
very important during the recruiting and hiring stages of employment. Suppose that
the committee of a company intends to choose a project manager from a group of