Linear Systems Over Pura Vida Neutrosophic Algebra

Rayyanu Abdullahi Muhammad, Department of Mathematics, Air Force Comprehensive School, Kwa, P.M.B: 3098, Kano, NigeriaFollow
Abdulhadi Aminu, Department of Mathematics, Aliko Dangote University of Science and Technology, Wudil, P.M.B: 3244, Kano, NigeriaFollow

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

Neutrosophic numbers offers a strong foundation for representing uncertainty, indeterminacy, and imprecision within mathematical systems. Pura Vida Neutrosophic Algebra (PVNA) expands upon max-plus algebra (also known as tropical algebra or path algebra) using neutrosophic numbers. In this study, we propose a novel extension of the Pura Vida Neutrosophic Algebra (PVNA) by formulating and analyzing linear systems within this algebraic context–an area that, to the best of our knowledge, has not been previously examined. Specifically, we introduce the concept of Neutrosophic Max-Plus Linear Systems, develop an algebraic methodology for their representation, and establish the necessary and sufficient conditions for the existence of solutions. This work significantly broadens the applicability of Pura Vida Neutrosophic algebra in addressing optimization problems characterized by uncertainty.

Keywords

Neutrosophic numbers, Max-plus algebra, Pura-vida neutrosophic algebra, Linear systems

How to Cite

Muhammad, Rayyanu Abdullahi and Aminu, Abdulhadi (2025) "Linear Systems Over Pura Vida Neutrosophic Algebra," Neutrosophic Systems with Applications: Vol. 25: Iss. 6, Article 3.