Methods for solving LR-bipolar fuzzy linear systems

Abstract

In this paper, we propose a technique to solve LR -bipolar fuzzy linear system(BFLS), LR -complex bipolar fuzzy linear (CBFL) system with real coefficients and LR -complex bipolar fuzzy linear (CBFL) system with complex coefficients of equations. Initially, we solve the LR -BFLS of equations using a pair of positive $$(*)$$ ( ∗ ) and negative $$(\\bullet )$$ ( ∙ ) of two $$n \\times n$$ n × n LR -real linear systems by using mean values and left-right spread systems. We also provide the necessary and sufficient conditions for the solution of LR -BFLS of equations. We illustrate the method by using some numerical examples of symmetric and asymmetric LR -BFLS equations and obtain the strong and weak solutions to the systems. Further, we solve the LR -CBFL system of equations with real coefficients and LR -CBFL system of equations with complex coefficients by pair of positive $$(*)$$ ( ∗ ) and negative $$(\\bullet )$$ ( ∙ ) two $$n \\times n$$ n × n real and complex LR -bipolar fuzzy linear systems by using mean values and left-right spread systems. Finally, we show the usage of technique to solve the current flow circuit which is represented by LR -CBFL system with complex coefficients and obtain the unknown current in term of LR -bipolar fuzzy complex number.