Solution of the fully fuzzy linear systems using the decomposition procedure

Dehghan, Mehdi; Hashemi, Behnam

doi:10.1016/j.amc.2006.05.043

Cited by 68 publications

(32 citation statements)

References 30 publications

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“…In this section, the limitations of the existing methods, for example, [2,[5][6][7][8][9][10][11][12][13][14][17][18][19][20][21][22][23][24][25][26][27][28][29] are pointed out.…”

Section: Limitations Of the Existing Methodsmentioning

confidence: 99%

“…Dehghan and Hashemi [12,13] proposed the Adomian decomposition method, and other iterative methods to find the positive fuzzy vector solution of n × n fully fuzzy linear system. Dehghan et al [14] proposed some computational methods such as Cramer's rule, Gauss elimination method, LU decomposition method and linear programming approach for finding the approximated solution of FFLS.…”

Section: Introductionmentioning

confidence: 99%

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A New Approach for Solving Fully Fuzzy Linear Systems

Kumar

Babbar

Bansal

2011

Advances in Fuzzy Systems

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Several authors have proposed different methods to find the solution of fully fuzzy linear systems (FFLSs) that is, fuzzy linear system with fuzzy coefficients involving fuzzy variables. But all the existing methods are based on the assumption that all the fuzzy coefficients and the fuzzy variables are nonnegative fuzzy numbers. In this paper a new method is proposed to solve an FFLS with arbitrary coefficients and arbitrary solution vector, that is, there is no restriction on the elements that have been used in the FFLS. The primary objective of this paper is thus to introduce the concept and a computational method for solving FFLS with no non negative constraint on the parameters. The method incorporates the principles of linear programming in solving an FFLS with arbitrary coefficients and is not only easier to understand but also widens the scope of fuzzy linear equations in scientific applications. To show the advantages of the proposed method over existing methods we solve three FFLSs.

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“…In this section, the limitations of the existing methods, for example, [2,[5][6][7][8][9][10][11][12][13][14][17][18][19][20][21][22][23][24][25][26][27][28][29] are pointed out.…”

Section: Limitations Of the Existing Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A New Approach for Solving Fully Fuzzy Linear Systems

Kumar

Babbar

Bansal

2011

Advances in Fuzzy Systems

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“…al. [5,6,7] has studied some methods for solving FFLS. They have represented fuzzy numbers in LR form and applied approximate operators between fuzzy numbers to find positive solutions of FFLS, so finding the solutions of FFLS is transformed to finding the solutions of three crisp systems.…”

Section: Introductionmentioning

confidence: 99%

The pseudo inverse matrices to solve general fully fuzzy linear systems

Moloudzadeh¹,

Darabi²,

Khandani³

2013

Journal of Soft Computing and Applications

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In this paper, we present a solution of an arbitrary general fully fuzzy linear systems (FFLS) in the form A ⊗ x = b. Where coefficient matrix A is an m × n fuzzy matrix and all of this system are elements of LR type fuzzy numbers. Our method discuss a general FFLS (square or rectangle fully fuzzy linear systems with trapezoidal or triangular LR fuzzy numbers). To do this, we transform fully fuzzy linear system in to two crisp linear systems, then obtain the solution of this two systems by using the pseudo inverse matrix method. Numerical examples are given to illustrate our method.

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“…He also shared a new method of using Linear Programming (LP) in order to obtain the solution of square and non-square matrix. The Adomian decomposition method was also expanded in order to solve the positive fuzzy vector solution of FFLS in [11]. Dehghan and Hashemi in [13] investigated the iterative solution like Gauss-Seidel, Jacobi and Jacobi over-relaxation (JOR).…”

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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Solution of the fully fuzzy linear systems using the decomposition procedure

Cited by 68 publications

References 30 publications

A New Approach for Solving Fully Fuzzy Linear Systems

A New Approach for Solving Fully Fuzzy Linear Systems

The pseudo inverse matrices to solve general fully fuzzy linear systems

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

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