In this manuscript, we focus on the brief study of finding the solution to and analyzingthe homogeneous linear difference equation in a neutrosophic environment, i.e., we interpreted the solution of the homogeneous difference equation with initial information, coefficient and both as a neutrosophic number. The idea for solving and analyzing the above using the characterization theorem is demonstrated. The whole theoretical work is followed by numerical examples and an application in actuarial science, which shows the great impact of neutrosophic set theory in mathematical modeling in a discrete system for better understanding the behavior of the system in an elegant manner. It is worthy to mention that symmetry measure of the systems is employed here, which shows important results in neutrosophic arena application in a discrete system.

中文翻译：

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中智齐次差分方程的解与解释

在这篇手稿中，我们专注于寻找和分析中智环境中齐次线性差分方程的解的简要研究，即我们将具有初始信息、系数和两者的齐次差分方程的解解释为中智数。演示了使用表征定理解决和分析上述问题的想法。整个理论工作之后是数值例子和在精算科学中的应用，展示了中智集合论在离散系统数学建模中的巨大影响，以便以优雅的方式更好地理解系统的行为。值得一提的是，这里采用了系统的对称性测度，这显示了在离散系统中的中智学领域应用中的重要结果。