A Generalized Cramer’s Rule for Tri- Component Interval-valued Neutrosophic Linear Systems

By: Khadija Sola

Department of Mathematics - Faculty of Science - University of Zawia

Issue: Vol 25 | First Issue | 2026

article language: English

Abstract:

This paper introduces a novel method for solving tri- component interval-valued Neutrosophic linear systems. Building upon fundamental concepts of Neutrosophic sets, including tri-component interval numbers and their algebraic operations, we first derive a generalized matrix representation for systems with n linear equations with m unknowns in this uncertain environment. The core contribution of this work is the development of a generalized Cramer’s rule tailored for these Neutrosophic systems, providing ananalytical framework for obtaining solutions under conditions of incompleteness, inconsistency, and indeterminacy. The efficacy and robustness of the proposed method are demonstrated through compassing numerical examples, encompassing binary\ and a generalized system cases. These examples illustrate all possible types of solution: unique solution, no solution, and infinitely many solutions. This research focuses on the theoretical and analytical aspects of solving Neutrosophic systems, relying on Cramer’s rule to find abstract mathematical solutions.

Keywords: Neutrosophic, Linear Systems, Determinants, Cramer's Rule, Libya.