It is an interesting alebra and it has exactly same algebraic properties of conventional algebra (R,+, .) Also thematrices canbe defined on this algbra where addition is max operation and multiplication is ordinaty addition in real numbers.

Yes it can ve used in operational research.

Dear Prof. Cenap Özel ,

I am interested in fuzzy matrix where addition is max operation.

Definition. Consider a matrixwhere aij ∈ [0,1], 1 ≤ i ≤ m and 1 ≤ j ≤ n. Then A is fuzzy matrix.

Operation maximum of matrices. Given two fuzzy matrices A = [ aij ](m,n)  and  B=  [ bij ]m,n) their sum is defined to be

          A⊕B = [ max(aij,bij) ](m,n).

          But the product of two fuzzy matrices under usual matrix multiplication is not a fuzzy matrix. Therefore we used the max-min operation for their product, as the following.

Operation max-min of matrices. Let A = [ aij ](m,p) and B = [ bij ](p,n) be two fuzzy matrices. Then their product, denoted by A⊗B, is defined to be the fuzzy matrix [ cij ](m,n), where  cij = max{min(aik,bkj)}.

Please see:

W.B.V. Kandasamy, F. Smarandache and K. Ilanthenral, Elementary Fuzzy Matrix Theory and Fuzzy Models for Social Scientists, Automaton, Los Angeles, 2007.

Regards,

Wiwat Wanicharpichat

Thanks for your valuable explanations dear profesor Wiwat. Plz write me yoyr email i will email to u a new paper related max-plus algebra.

Thank you for your kindness. My email:

[email protected]

• Please mind my new added question dear profesor wiwat and checkbyour email account.

We can do collobrations