Optimizing Range Norm of The Image Set of Matrix over Interval Max-Plus Algebra with Prescribed Components

Let be the set of all real numbers and _ε = ⋃ {ε} whose ε = –∞. Max-plus algebra is the set _ε that is equipped two operations maximum and addition. It can be formed matrices in the size of m × n whose elements belong to _ε, called matrix over max-plus algebra. Optimizing range norm of the image set of matrix over max-plus algebra with prescribed components has been discussed. Interval Max-Plus Algebra is the set $I{(}_{{\mathbb{R}}}=\{\text{x}=[\mathop{\_}\limits_{},\text{x¯}]|\text{x\_},\text{x¯}\in {\mathbb{R}},\varepsilon \lt \text{x\_}\le \text{x¯}\}\cup \{\text{ε}\}$ with ε = [ε, ε], is equipped with two operations maximum $(\bar{\oplus })$ and addition $(\bar{\otimes })$. The set of all matrices in the size of m × n whose elements belong to I()_ε, called matrix over interval max-plus algebra. Optimizing range norm of the image set of matrix over interval max-plus algebra has been discussed. In this paper, we will discuss optimizing range norm of the image set of matrix over interval max-plus algebra with prescribed components.