Intuitionistic Fuzzy IMs - Index Matrices: Towards an Augmented Matrix Calculus - page 38

where

⎧
⎨

k k

K ∗ ) μ k i , l j ,ν k i , l j , if k i ,α

i ,β i ∈

N ρ 1 ,σ 1 (

l l

L ∗ ) and l j ,α

j ,β j ∈

N ρ 2 ,σ 2 (

and μ k i , l j ≥ ρ 3 & ν k i , l j ≤ σ 3

ϕ k i , l j ,ψ k i , l j = ,

⎩

k k

K ∗ )

0 , 1 , if k i ,α

i ,β i ∈

N

ρ 1 ,σ 1 (

l l

L ∗ ) and l j ,α

j ,β j ∈

N ρ 2 ,σ 2 (

and μ k i , l j <ρ 3 ∨ ν k i , l j >σ 3

2.6 Aggregation Operations Over EIFIMs

Let the EIFIM

l l l l l l

l 1 , α

1 ,β 1

... l j , α

j ,β j

... l n , α

n ,β n

k k

k 1 , α

1 ,β 1 μ k 1 , l 1 ,ν k 1 , l 1 ... μ k 1 , l j ,ν k 1 , l j ... μ k 1 , l n ,ν k 1 , l n

. . . .

. . . . . .

A = ,

k k

k i , α

i ,β i

μ k i , l 1 ,ν k i , l 1 ... μ k i , l j ,ν k i , l j ... μ k i , l n ,ν k i , l n

. . . .

. . . . . .

m ,β m μ k m , l 1 ,ν k m , l 1 ... μ k m , l j ,ν k m , l j ... μ k m , l n ,ν k m , l n

k m , α

be given and let k 0 ∈ L be two fixed indices.

Now, we introduce the following 18 operations over it.

K and l 0 ∈

(max,max)-row-aggregation

ρ ( max , max ) ( A , k 0 )

l l

l 1 , α

1 ,β 1

...

= k k

k 0 , max

m α

i ,

min

m β

i

max

m μ k i , l 1 ,

min

m ν k i , l 1 ...

1 ≤ i ≤ 1 ≤ i ≤ 1 ≤ i ≤ 1 ≤ i ≤

l n ,β n

... l n , α

m ν k i , l n ,

... max

1 m μ k i , l n ,

min

≤ i ≤ 1 ≤ i ≤

(max,ave)-row-aggregation

ρ ( max , max ) ( A , k 0 )

l l

l 1 , α

1 ,β 1

...

i = 1 μ k i , l 1 ,

m

i = 1 ν k i , l 1 ...

m

=

k k 1

m

1
m

k 0 , max

1 m α

i ,

min

m β

i

≤ i ≤ 1 ≤ i ≤