Intuitionistic Fuzzy Aggregation Techniques - Intuitionistic Fuzzy Aggregation and Clustering - page 99

The deviation values between the FIFWA and FIFWG operators

Fig. 1.17 The deviation values for alternatives between the FIFWA and FIFWG operators

1.7 Generalized Intuitionistic Fuzzy Aggregation Operators
Based on Hamacher t-conorm and t-norm

Yager (2004) proposed the generalized ordered weighted aggregation operators,
which give the aggregated arguments a function and a corresponding reverse function
to the arguments after being aggregated, and as the function changes, a family of
aggregation operators can be obtained. Based on this useful idea and using the basic
operations given in Definition 1.21, in this section, we shall introduce the generalized
intuitionistic fuzzy aggregations based on Hamacher t-conorm and t-norm.
Let

α i = (μ α i , v α i )( i = 1 , 2 ,..., n ) be a collection of IFVs and w =

T

( w 1 , w 2 , ..., w n ) the weight vector of α i ( i = 1 , 2 ,..., n ) , where w i indicates

and i = 1 w i the importance degree of 1.

Then based on Eqs. ( 1.194 ), ( 1.195 ), and Definition 1.21, we define the following:

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

Definition 1.24 (Xia and Xu 2011) If

n
⊕ w i α i

1
λ

GHIFWA (α 1 ,α 2 ,...,α n ) = (1.242)

i = 1

then GHIFWA is called a generalized Hamacher intuitionistic fuzzy averaging
(GHIFWA) operator.