Abstract
This paper introduces a concept of AE solutions to two-sided interval max-plus linear systems, a rather general concept which includes many known concepts of solutions to interval systems, in particular, weak, strong, tolerance and control solutions as its special cases. We state full characterizations of AE solutions for the two-sided interval max-plus systems, including both linear inequalities and linear equations. Moreover, we provide a specific example to illustrate an efficient method of finding the AE solution set.
Highlights
The max-plus algebra (Rmax, ⊕, ⊗) has appeared under the name extremal algebra for many years [1, 2]
Shary first proposed the concept of AE solutions for interval linear equations in 2002, a rather general concept which includes many traditional concepts of solutions to interval systems as its special cases [19]
We extend the concept of AE solutions of an interval linear system in classical algebra to the max-plus algebra
Summary
The max-plus algebra (Rmax, ⊕, ⊗) has appeared under the name extremal algebra for many years [1, 2]. A sufficient and necessary characterization of AE solutions to interval system of maxplus linear inequalities (2.1) is described in the following theorem. Theorem 4.1 A vector x ∈ Rnmax is an AE solution of two-sided interval linear max-plus inequalities (2.1) if and only if
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
