AE solutions to interval max-plus matrix equations

Abstract

Max-plus algebra is an algebraic structure which classical addition and multiplication are replaced by the operations ⊕ and ⊗. This study extends the concepts of AE solutions for interval linear system to AE solutions for interval matrix equations (IME) within the framework of max-plus algebra. The research provides a comprehensive characterization of AE solutions to interval matrix equations, covering both linear inequalities and linear equations. It introduces general framework that includes specific solution types- weak, strong, tolerance and control solutions-as special cases, encompassing many known solution concepts for interval max-plus matrix equations. Additionally, the study presents specific examples to demonstrate an efficient method for verifying AE solutions to interval max-plus matrix equations (MPME) and highlights results for the various solution types, including weak, strong, tolerance and control solutions.