Solving Fully Fuzzy Linear System with the Necessary and Sufficient Condition to have a Positive Solution

Abstract

This paper proposes new matrix methods for solving positive solutions for a positive Fully Fuzzy Linear System (FFLS). All coefficients on the right hand side are collected in one block matrix, while the entries on the left hand side are collected in one vector. Therefore, the solution can be gained with a non-fuzzy common step. The necessary theorems are derived to obtain a necessary and sufficient condition in order to obtain the solution.The solution for FFLS is obtained where the entries of coefficients are unknown. The methods and results are also capable of solving Left-Right Fuzzy Linear System (LR-FLS). To best illustrate the proposed methods, numerical examples are solved and compared to the existing methods to show the efficiency of the proposed method. New numerical examples are presented to demonstrate the contributions in this paper.

A Note on “Solving Fully Fuzzy Linear Systems by Using Implicit Gauss–Cholesky Algorithm”

“…X g are provided using the methods in [9,10]. (4, 3, 2) ⊗ (x 1 , y 1 , z 1 ) ⊗ (5, 2,1) ⊗ (x 2 , y 2 , z 2 ) ⊗ (3, 0, 3) ⊗ (x 3 , y 3 , z 3 ) = (71, 54, 76), (7,4,3) ⊗ (x 1 , y 1 , z 1 ) ⊗ (10, 6, 3) ⊗ (x 2 , y 2 , z 2 ) ⊗ (2,1,1) ⊗ (x 3 , y 3 , z 3 ) = (118,115,129), (6, 2, 2) ⊗ (x 1 , y 1 , z 1 ) ⊗ (7,1, 2) ⊗ (x 2 , y 2 , z 2 ) ⊗ (15, 5, 4) ⊗ (x 3 , y 3 , z 3 ) = (155, 89,151).…”

Algebraic Modification of Trapezoidal Fuzzy Numbers to Complete Fully Fuzzy Linear Equations System Using Gauss-Jacobi Method

“…The method can be used in solving linear equation system in fuzzy numbers is divided into direct and indirect methods. Completion of the fully fuzzy linear equation system discussed by other researchers which is Sri [5] discusses fuzzy trapezoidal numbers using the QR decomposition method. Kumar et al [9] applies a new method to the fuzzy trapezoidal number named Mehar method and J Kaur et al [11] has comentary on "calculating fuzzy inverse matrix using fuzzy linear syatem".…”

A new solution of pair matrix equations with arbitrary triangular fuzzy numbers

“…The main contribution of this study would be the improvement of the associated linear system that was originally constructed in [22]. Besides that, the fuzzy Kronecker product and fuzzy V ec -operator are also utilized in this algorithm to convert the PFFME into a simpler form of equations.…”