Certain methods to solve bipolar fuzzy linear system of equations

Abstract

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.