Intuitionistic Fuzzy IMs - Index Matrices: Towards an Augmented Matrix Calculus - page 42

(ave,min)-column-aggregation

j = 1 α

n

j = 1 β

n

1
n

l 1

n

l

l 0 ,

j , j

k k

k 1 , α

1 ,β 1

min

n μ k 1 , l j ,

max
1 n ν k 1 , l j

σ max ( A , l 0 ) = ,

1 ≤ j ≤ ≤ j ≤

. .

k k

k m , α

m ,β m

min

n μ k m , l j ,

max
1 n ν k m , l j

1 ≤ j ≤ ≤ j ≤

(min,max)-column-aggregation

l l

l 0 , min

m α

j ,

max
1 m β

j

1 ≤ i ≤ ≤ i ≤

k k

k 1 , α

1 ,β 1

max
1 n μ k 1 , l j ,

min

n ν k 1 , l j

≤ j ≤ 1 ≤ j ≤

σ max ( A , l 0 ) = ,

. .

k k

k m , α

m ,β m

max

n μ k m , l j ,

min

n ν k m , l j

1 ≤ j ≤ 1 ≤ j ≤

(min,ave)-column-aggregation

l l

l 0 , min

m α

j ,

max
1 m β

j

1 ≤ i ≤ ≤ i ≤

j = 1 μ k 1 , l j ,

n

j = 1 ν k 1 , l j

n

1
n

1
n

k k

k 1 , α

1 ,β 1

σ max ( A , l 0 ) = ,

. .

j = 1 μ k m , l j , j = 1 ν k m , l j

n n

1
n

1
n

m ,β m

k m , α

(min,min)-column-aggregation

l l

l 0 , min

≤ i ≤ m α

j ,

max
1 ≤ i ≤ m β

j

1

k k

k 1 , α

1 ,β 1

min

n μ k 1 , l j ,

max
1 n ν k 1 , l j

1 ≤ j ≤ ≤ j ≤

σ max ( A , l 0 ) = .

. .

m m

k m , α ,β min

≤ j ≤ n μ k m , l j ,

max
1 ≤ j ≤ n ν k m , l j 1