Homomorphic solution of fully fuzzy linear systems

Allahviranloo, Tofigh; Kiani, Narsis A.; Barkhordary, M.; Mosleh, Maryam

doi:10.1007/s10598-008-9004-z

Cited by 13 publications

(21 citation statements)

References 28 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%

“…Nasseri et al [17] used certain decomposition methods of the coefficient matrix for solving fully fuzzy linear system of equations. Allahviranloo et al [18] proposed a numerical method for solving FFLS Ax = b, when coefficient matrix is positive. Gao [19] proposed a unified iterative scheme for solving nonsquare FFLS with nonnegative constraints.…”

Section: Advances In Fuzzy Systemsmentioning

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: Advances In Fuzzy Systemsmentioning

confidence: 99%

A New Approach for Solving Fully Fuzzy Linear Systems

Kumar

Babbar

Bansal

2011

Advances in Fuzzy Systems

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“…Rao and Chen [24] considered the numerical solutions of FLSs in engineering analysis. Allahviranloo et al proposed the fuzzy symmetric solutions and other algebraic solution for fuzzy linear systems [6,11], and the solutions of fully fuzzy linear systems [8,9,10,12,18,19,23]. Friedman et al [21] suggested a general model for solving a class of n × n FLSs        a 11 x 1 + a 12 x 2 + · · · + a 1n x n = y 1 ,…”

Section: Introductionmentioning

confidence: 99%

Uzawa method for fuzzy linear system

Wang¹

2013

Journal of Fuzzy Set Valued Analysis

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An Uzawa method is presented for solving fuzzy linear systems whose coefficient matrix is crisp and the right-hand side column is arbitrary fuzzy number vector. The explicit iterative scheme is given. The convergence is analyzed with convergence theorems and the optimal parameter is obtained. Numerical examples are given to illustrate the procedure and show the effectiveness and efficiency of the method.

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“…Indeed, Dehghan et al proposed iterative techniques such as Richardson, Jacobi, Jacobi overrelaxation (JOR), Gauss-Seidel, successive overrelaxation (SOR), accelerated overrelaxation (AOR), symmetric and unsymmetric SOR (SSOR and USSOR), and extrapolated modified Aitken (EMA) for solving FFLS in [8]. Allahviranloo et al proposed the homomorphic solution in the canonical trapezoidal form of FFLS based on three parameters, value, ambiguity, and fuzziness, in [5].…”

Section: Introductionmentioning

confidence: 99%

“…In recent papers, [5,7,8], the n × n FFLS was replaced by three n × n crisp linear systems, then the authors tried to solve these systems. In this paper, we use the implicit Gauss-Cholesky (IGC) algorithm of ABS class to solve only one of these three crisp systems and obtain the solutions of another two crisp systems by the perturbation technique.…”

Section: Introductionmentioning

confidence: 99%