Solving fully fuzzy linear systems by using implicit Gauss–Cholesky algorithm

“…In this section, we will discuss the proposed solutions in [1]. We also show that they do not correspond to the systems by applying arithmetic operations on LR fuzzy numbers to prove that !…”

Section: Numerical Examplesmentioning

confidence: 99%

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

et al. 2015

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“…Dehghan and his colleagues [10][11][12][13] obtained the solution for FFLS where the coefficient and parameters are positive. Furthermore, for the same scenario, several scholars [1,17,[34][35][36][37][38] suggested new methods for solving FFLS in a similar way to Dehghan. Malkawi and his colleagues [26][27][28] recommended new matrix methods for solving a positive FFLS.…”

Section: Introductionmentioning

confidence: 99%

An Algorithm for a Positive Solution of Arbitrary Fully Fuzzy Linear System

2015

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This paper proposes a new computational method to obtain a positive solution for arbitrary fully fuzzy linear system (FFLS). The new method transforms the coefficients in FFLS to a one-block matrix. As a result, none of the fuzzy operations are needed. This method can provide a solution regardless of the size of a system. Some necessary theorems are proved and new numerical examples are presented to illustrate the proposed method.

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“…Few researchers commented on new methods to solve FFLS [21][22][23][24][25], and brought forward new methods to solve FFLS. However, Kumar et al [4] introduced a new computational method to solve FFLS by relying on the computation of row reduced echelon form.…”

Section: Introductionmentioning

confidence: 99%

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

Malkawi¹,

Ahmad²,

Ibrahim³

2014

Appl. Math. Inf. Sci.

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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.

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Solving fully fuzzy linear systems by using implicit Gauss–Cholesky algorithm

Abstract: This paper analyzes the solution to fully fuzzy linear systems (FFLS). To do so, the implicit GaussCholesky algorithm (IGC) of ABS class is used. Indeed FFLS with different right hand-sides are considered.

Cited by 11 publications

References 12 publications

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

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

An Algorithm for a Positive Solution of Arbitrary Fully Fuzzy Linear System

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

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