On the algebraic solution of fuzzy linear systems based on interval theory

Allahviranloo, Tofigh; Ghanbari, M.

doi:10.1016/j.apm.2012.01.002

Cited by 52 publications

(30 citation statements)

References 29 publications

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“…In [49], via a 2-step procedure, the authors computed the maximal and minimal symmetric solution of the FEVP. Lately in [3], Allahviranloo and Hooshangian proposed a bilateral scheme, where the 1-cut of the problem is first solved and then unknown symmetric spreads are allocated to each row of the 1-cut system. The authors used the standard determinant technique to solve the 1-cut system.…”

Section: Introductionmentioning

confidence: 99%

Krylov subspace method for fuzzy eigenvalue problem

Kanaksabee

Dookhitram

Bhuruth

2014

Journal of Intelligent &Amp; Fuzzy Systems

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The eigenvalue problem arises in many application areas and in the fuzzy setting, focus has always been geared towards the finding of solution for the whole set of eigenvalues and corresponding eigenvectors. This paper introduces the computation of a few eigenpairs of a matrix with triangular fuzzy numbers as elements, where the modal matrix is assumed to be sparse and real symmetric. A two-step procedure is developed for the solution of this type of fuzzy eigenvalue problem. The first step solves the 1-cut of the problem, where the well-known Krylov subspace method, implicitly restarted Lanczos algorithm, is employed to approximate part of the spectrum with respect to either smallest or largest eigenvalues. The second step assigns unknown symmetric linear spreads to the approximate eigenpairs. Numerical experiments are provided to illustrate the efficiency of the proposed scheme for determining fuzzy symmetric eigenpairs of a fuzzy matrix.

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Section: Introductionmentioning

confidence: 99%

Krylov subspace method for fuzzy eigenvalue problem

Kanaksabee

Dookhitram

Bhuruth

2014

Journal of Intelligent &Amp; Fuzzy Systems

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“…Also, in [9,10], Abbasbandy et al proposed the LU-decomposition method and the Steepest descent method to solve system, respectively. For more research see [11][12][13][14][15][16][17][18][19][20][21][22].…”

Section: Introductionmentioning

confidence: 99%

General Solutions of Fully Fuzzy Linear Systems

Allahviranloo

Salahshour

Homayoun-nejad

et al. 2013

Abstract and Applied Analysis

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We propose a method to approximate the solutions of fully fuzzy linear system (FFLS), the so-calledgeneral solutions. So, we firstly solve the 1-cut position of a system, then some unknown spreads are allocated to each row of an FFLS. Using this methodology, we obtain some general solutions which are placed in the well-known solution sets like Tolerable solution set (TSS) and Controllable solution set (CSS). Finally, we solved two examples in order to demonstrate the ability of the proposed method.

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“…Recently, he and Salahshour in [10] proposed a simple and practical method to obtain fuzzy symmetric solutions of fuzzy linear systems. The algebraic solution of such systems and its properties are discussed in [8]. Also Ghanbari and his colleague in [15] have proposed an approach for computing the general compromised solution of an L-R fuzzy linear system by use of a ranking function when the coefficient matrix is a crisp m × n matrix.…”

Section: Introductionmentioning

confidence: 99%

On the global solution of a fuzzy linear system

Allahviranloo¹,

Skuka²,

Tahvili³

2014

Journal of Fuzzy Set Valued Analysis

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The global solution of a fuzzy linear system contains the crisp vector solution of a real linear system. So discussion about the global solution of a n × n fuzzy linear system Ax =b with a fuzzy number vector b in the right hand side and crisp a coefficient matrix A is considered. The advantage of the paper is developing a new algorithm to find the solution of such system by considering a global solution based upon the concept of a convex fuzzy numbers. At first the existence and uniqueness of the solution are introduced and then the related theorems and properties about the solution are proved in details. Finally the method is illustrated by solving some numerical examples.

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On the algebraic solution of fuzzy linear systems based on interval theory

Cited by 52 publications

References 29 publications

Krylov subspace method for fuzzy eigenvalue problem

Krylov subspace method for fuzzy eigenvalue problem

General Solutions of Fully Fuzzy Linear Systems

On the global solution of a fuzzy linear system

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