Interval Strong Solutions of Interval Systems of Max-Plus Linear Equations

Fathin Azkiya

doi:10.22146/jmt.66309

Interval Strong Solutions of Interval Systems of Max-Plus Linear Equations

https://doi.org/10.22146/jmt.66309

Fathin Azkiya^(1*)

(1) Gadjah Mada University
(*) Corresponding Author

Abstract

Let R be the set of all real numbers and Rε = R ∪ {ε} whose ε = {−∞}. Max-plus algebra is the set Rε that is equipped two operations maximum and addition. Max-plus algebra can be expanded to interval max-plus algebra, it is the set of closed intervals in Rε that is equipped with the operation maximum as ⊕ and the operation addition as ⊗ . This study aims to discuss the existence and uniqueness of interval strong solutions of interval systems of interval max-plus linear equations. The proof of the existence of interval strong solutions is constructive and generates a formula for computing such solutions. A necessary and sufficient condition for the uniqueness of interval strong solutions is obtained by testing the uniqueness of the solution of a finite number of subsystems from all of its subsystems. From these conditions, an algorithmcan be obtained that can verify the uniqueness of interval strong solutions of interval systems of max-plus linear equation

Keywords

Max-plus linear equation, interval system, strong solvable, interval strong solution.

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References

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DOI: https://doi.org/10.22146/jmt.66309