ORCID
Muhammad Rayyanu Abdullahi: https://orcid.org/0009-0002-6067-5619
Abdulhadi Aminu: https://orcid.org/0000-0003-1128-3010
Article Type
Research Article
Abstract
This paper proposes a neutrosophic extension of max-plus algebra for solving mixed systems of linear equations and inequalities.Classical max-plus algebra is a powerful tool for modeling synchronization in discrete-event systems LastNatpreClose LastNatClose, but it assumes fully deterministic data.To incorporate uncertainty and indeterminacy, we reformulate the framework so that coefficients and variables are expressed as neutrosophic numbers
γ+λI,γ,λ∈ℝ,I∈[0,1],
where I quantifies the degree of indeterminacy.
We redefine the max-plus semiring in this neutrosophic setting, extend solvability and uniqueness results, and adapt the ONEMLP-EI algorithm LastNatpreClose LastNatClose to handle neutrosophic optimization.A sensitivity analysis demonstrates robustness under parameter perturbations, complementing recent advances in neutrosophic linear programming and decision-making under uncertainty LastNatpreClose LastNatClose.Through a numerical example and a compact case study, we illustrate the feasibility, non-uniqueness, and optimization capabilities of the framework.
Applications in scheduling and production systems, under incomplete information, highlighting the novelty and practical value of neutrosophic max-plus modeling.
Keywords
Neutrosophic numbers, Max-plus algebra, Pura Vida neutrosophic algebra, Mixed linear equation–inequality systems, Sensitivity analysis
How to Cite
Abdullahi, Muhammad Rayyanu and Aminu, Abdulhadi
(2025)
"Mixed Linear Equation–Inequality Systems over the Pura Vida Neutrosophic Algebra,"
Neutrosophic Systems with Applications: Vol. 25:
Iss.
12, Article 4.
DOI: https://doi.org/10.63689/2993-7159.1312
