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l
l
l 0 ,
n α
j ,
n β
j
1
j
1
j
k
1
k
1
k 1 , α
, β
n μ k 1 , l j ,
n ν k i , l j
=
| τ T
.
1
j
1
j
.
.
k m
m
k m , α
, β
n μ k m , l j ,
n ν k i , l j
1
j
1
j
Let
and
be two other dual operations, that can coincide with
( , )
or
( , )
,
or to be different. The following new aggregation operation can be defined:
( , , ) T
-aggregation
ρ ( , , ) (
A (T ))
l
1
l
1
l 1 ,
τ T α
,
τ T β
...
k
1
k
1
k 1 ,
τ T α
,
τ T β
τ T μ k 1 , l 1 ,
τ T ν k 1 , l 1 ...
=
.
. .
...
k m ,
k m
m
τ T α
,
τ T β
τ T μ k m , l 1 ,
τ T ν k m , l 1 ...
l n
l n
...
l n , α
, β
...
τ T μ k 1 , l n ,
τ T ν k 1 , l n
.
.
.
...
τ T μ k m , l n ,
τ T ν k m , l n
The above operations are extensions of the operations from IFIMs, EIFIMs and
TIFIMs and have similar properties.
 
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