In this article, we present two different analytical methods based on embedding technique and bipolar fuzzy center to solve bipolar fuzzy linear system (BFLS) of equations. In the first method, to solve BFLS of equations, we replace BFLS of equations by a pair of positive\((*)\) and negative\((\bullet )\) two \(n \times n\) crisp linear systems. We provide the necessary and sufficient conditions for the solution of BFLS of equations. In the second method, we use the graphical technique and apply bipolar fuzzy center to draw a graph at some specific end points to solve the BFLS of equations. Further, we develop a technique to solve the fully bipolar fuzzy linear system of equations. We present solutions of some numerical examples to show the effectiveness of the proposed techniques.

中文翻译：

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求解双极模糊线性方程组的某些方法

在本文中，我们提出了两种基于嵌入技术和双极模糊中心的解析方法来求解双极模糊线性系统（BFLS）。在第一种方法中，为求解方程的BFLS，我们用一对正\（（*）\）和负\（（\ bullet）\）两个\ {n \ times n \}替换方程的BFLS。清晰的线性系统。我们为方程BFLS的求解提供了充要条件。在第二种方法中，我们使用图形技术并应用双极模糊中心在某些特定端点绘制图形以求解方程的BFLS。此外，我们开发了一种解决方程组的完全双极模糊线性系统的技术。我们提供一些数值示例的解决方案，以显示所提出技术的有效性。