Closure of the simple image set of linear mapping interval max-plus
Siswanto Siswanto, Vika Yugi Kurniawan, Pangadi, B. W. Santoso · Journal of Discrete Mathematical Sciences and Cryptography · 2020
Max-plus algebra is a set ℝe = ℝ ∪ {ε }, where ℝ is a set of all real numbers that is equipped with operations ⊕ and ⊗. For each a, b ϵ ℝ operations ⊕ and ⊗ are defined as a ⊕ b = max(a, b) and a ⊗ b = a + b. The set matrices of size m × n whose elements are element of ℝe is called the matrices over ℝe and denoted as . Given the system of linear equations A ⊗ x = b with A ⊗ x = b, with and . The concept of the simple image set of strongly regular matrices is related to the concept of linear equations systems. It has been discussed about closure of the simple image set of strongly regular matrices over max-plus algebra. Interval max-plus algebra is an extension of max-plus algebra. The purpose of this research is to determine closure of the simple image set of strongly regular matrices which is image of k-iteration the matrix after the matrix is normalized. Matrices that is discussed is matrices over interval max-plus algebra.