Intuitionistic Fuzzy IMs - Index Matrices: Towards an Augmented Matrix Calculus - page 32

2.3 Standard Operations Over EIFIMs

K ∗ , L ∗ , { μ k i , l j ,ν k i , l j }] , P ∗ , Q ∗ , { ρ p r , q s ,σ p r , q s }]

For the EIFIMs A ,

operations that are analogous to the usual matrix operations of addition and multi-
plication are defined, as well as other specific ones.

=[ B =[

Addition-(max,min)

T ∗ , V ∗ , { ϕ t u ,v w ,ψ t u ,v w }] ,

A ⊕ ( max , min ) B =[

where

T ∗ = K ∗ ∪ P ∗ ={

t t

t u ,α

u ,β u |

t u ∈ K ∪ P } ,

V ∗ = L ∗ ∪ Q ∗ ={ v w ,α w ,β w | v w ∈ L ∪ Q } ,

⎧
⎨

k

α

i ,

if t u ∈ K − P

r

t u

α = α ,

if t u ∈

− ,

P K

⎩

p
r

k

max (α

i ,α

), if t u ∈ K ∩ P

⎧
⎨

l

β

j ,

if v w ∈ L − Q

q
s

β w = β , if t w ∈ Q − L ,

⎩

q
s

l

min (β

j ,β

), if t

w ∈

L ∩ Q

and

⎧
⎨

μ k i , l j ,ν k i , l j , if t u = k i ∈ K

and v w = l j ∈ L − Q

or t u = k i ∈ K − P

and v w = l j ∈ L ;

ρ p r , q s ,σ p r , q s , if t u = p r ∈ P

and v w = q s ∈ Q − L

ϕ t u ,v w ,ψ t u ,v w =

⎩ or t u = p r ∈ P − K

and v w = q s ∈ Q ;

(μ k i , l j ,ρ p r , q s ),

if t u =

= ∈ ∩

max k i p r K P

min (ν k i , l j ,σ p r , q s ) , and v w = l j = q s ∈ L ∩ Q

0 , 1 , otherwise