Intuitionistic Fuzzy Aggregation Techniques - Intuitionistic Fuzzy Aggregation and Clustering - page 78

Table 1.12 Intuitionistic fuzzy decision matrix B

G 1 G 2 G 3 G 4

y 1 ( 0 . 33 , 0 . 33 , 0 . 34 ) ( 0 . 22 , 0 . 34 , 0 . 44 ) ( 0 . 23 , 0 . 49 , 0 . 28 ) ( 0 . 15 , 0 . 57 , 0 . 28 )

y 2 ( 0 . 24 , 0 . 34 , 0 . 42 ) ( 0 . 26 , 0 . 40 , 0 . 34 ) ( 0 . 21 , 0 . 28 , 0 . 51 ) ( 0 . 44 , 0 . 39 , 0 . 17 )

y 3 ( 0 . 11 , 0 . 16 , 0 . 73 ) ( 0 . 19 , 0 . 47 , 0 . 34 ) ( 0 . 23 , 0 . 31 , 0 . 46 ) ( 0 . 35 , 0 . 46 , 0 . 19 )

y 4 ( 0 . 19 , 0 . 38 , 0 . 43 ) ( 0 . 31 , 0 . 29 , 0 . 40 ) ( 0 . 44 , 0 . 24 , 0 . 32 ) ( 0 . 21 , 0 . 25 , 0 . 54 )

y 5 ( 0 . 37 , 0 . 48 , 0 . 15 ) ( 0 . 29 , 0 . 39 , 0 . 32 ) ( 0 . 32 , 0 . 35 , 0 . 33 ) ( 0 . 34 , 0 . 25 , 0 . 41 )

y 6 ( 0 . 25 , 0 . 34 , 0 . 41 ) ( 0 . 24 , 0 . 35 , 0 . 41 ) ( 0 . 30 , 0 . 28 , 0 . 42 ) ( 0 . 45 , 0 . 28 , 0 . 27 )

candidates. Project management is the application of knowledge, skills, tools, and
techniques to the implementation of project activities for the purpose of meeting
project requirements. The requirements of a project manager are not only morale,
but also proficiency in project management. Suppose that four attributes: (1) G 1 (self-
confidence); (2) G 2 (personality); (3) G 3 (past experience); and (4) G 4 (proficiency
in project management), are taken into consideration in the selection problem and
there exist six candidates y i

. Assume that the performance of
the alternative y i with respect to the attribute G j is measured by an IFV b ij

( i = 1 , 2 ,..., 6 )

=

(μ ij , v ij ,π ij ) , and then we construct the intuitionistic fuzzy decision matrix B =

( b ij ) 6 × 4 (see Table 1.12 ) (Xia et al. 2012b).

To get the optimal alternative(s), the following steps are given (Xia et al. 2012b):

( = , , , )

Step 1 Considering all the attributes G j j 1 2 3 4 are the benefit attributes,

( = , ,..., )

the performance values of the alternatives y i i 1 2 6 do not need normal-

ization.
Step 2 Aggregate all the performance values r ij ( )

of the i th line, and get the overall performance value r i corresponding to the alter-
native y i by the GIFWBM (without of generalization, let p

i = 1 , 2 , 3 , 4 ; j = 1 , 2 ,..., 6

= q = r = 1 ) :

r 1 = ( 0 . 2061 , 0 . 4744 , 0 . 3195 ), r 2 = ( 0 . 3156 , 0 . 3532 , 0 . 3312 )

r 3 = ( 0 . 2583 , 0 . 3841 , 0 . 3576 ), r 4 = ( 0 . 2975 , 0 . 2673 , 0 . 4352 )

r 5 = ( 0 . 3270 , 0 . 3291 , 0 . 3439 ), r 6 = ( 0 . 3435 , 0 . 2997 , 0 . 3568 )

Step 3 Calculate the scores of all the alternatives:

S ( r 1 ) =− 0 . 2683 , S ( r 2 ) =− 0 . 0376 , S ( r 3 ) =− 0 . 1259

S ( r 4 ) = 0 . 0303 , S ( r 5 ) =− 0 . 0021 , S ( r 6 ) = 0 . 0439

Since

S ( r 6 )> S ( r 4 )> S ( r 5 )> S ( r 2 )> S ( r 3 )> S ( r 1 )

then by Xu and Yager (2006)'s ranking method, we get the ranking of the IFVs:

r 6 > r 4 > r 5 > r 2 > r 3 > r 1