Open AccessOptimizing Range Norm of The Image Set of Matrix over Interval Max-Plus Algebra with Prescribed Components
Author(s) -
Siswanto Siswanto,
Ari Suparwanto,
M. Andy Rudhito
Publication year - 2019
Publication title -
journal of physics. conference series
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.21
H-Index - 85
eISSN - 1742-6596
pISSN - 1742-6588
DOI - 10.1088/1742-6596/1306/1/012051
Subject(s) - algorithm , artificial intelligence , computer science
Let ℝ be the set of all real numbers and ℝ ε = ℝ ⋃ {ε} whose ε = –∞. Max-plus algebra is the set ℝ ε that is equipped two operations maximum and addition. It can be formed matrices in the size of m × n whose elements belong to ℝ 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 ( ℝ ) ε = { x = [ x _ , x ¯ ] | x _ , x ¯ ∈ ℝ , ε < x _ ≤ x ¯ } ∪ { ε } with ε = [ε, ε], is equipped with two operations maximum ( ⊕ ¯ ) and addition ( ⊗ ¯ ) . The set of all matrices in the size of m × n whose elements belong to I (ℝ) 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.