Affiliations: [a] Department of Mathematics, University of the Punjab, New Campus, Lahore, Pakistan
| [b]
Bahcesehir University, Faculty of Engineering and Natural Sciences, Istanbul, Turkey
| [c] Department of Mathematics, King Abdulaziz University, Jeddah, Saudi Arabia
Correspondence:
[*]
Corresponding author. Nawab Hussain, Department of Mathematics, King Abdulaziz University P.O Box 80203, Jeddah 21589, Saudi Arabia. E-mail: [email protected].
Abstract: The aim of this work is to solve the linear system of equations using LU decomposition method in bipolar fuzzy environment. We assume a special case when the coefficient matrix of the system is symmetric positive definite. We discuss this point in detail by giving some numerical examples. Moreover, we investigate m × n inconsistent bipolar fuzzy matrix equation and find the least square solution of the inconsistent bipolar fuzzy matrix using the generalized inverse matrix theory. The existence of the strong bipolar fuzzy least square solution of the inconsistent bipolar fuzzy matrix is discussed. In the end, a numerical example is presented to illustrate our proposed method.
Keywords: LU decomposition method, symmetric positive definite matrix, inconsistent bipolar fuzzy matrix equations, bipolar fuzzy least square solution
