A Unified Iterative Scheme for Solving Fully Fuzzy Linear System

Gao, Jing; Zhang, Qiang

doi:10.1109/gcis.2009.114

Cited by 12 publications

(10 citation statements)

References 11 publications

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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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Section: Introductionmentioning

confidence: 99%

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

2015

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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%

“…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%

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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“…This system is solved in [8,9] using decomposition of the coefficient matrix. Some other methods used iterative methods for solving FFLS [3,10,11]. Many researchers studied FFLS and numerical techniques to solve them [12][13][14][15][16].…”

Section: Introductionmentioning

confidence: 99%

An Application of Interval Arithmetic for Solving Fully Fuzzy Linear Systems with Trapezoidal Fuzzy Numbers

Siahlooei

Fazeli

2018

Advances in Fuzzy Systems

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We present a method for solving fully fuzzy linear systems using interval aspects of fuzzy numbers. This new method uses a decomposition technique to convert a fully fuzzy linear system into two types of decomposition in the form of interval matrices. It finds the solution of a fully fuzzy linear system by using interval operations. This new method uses interval arithmetic and two new interval operations ⊖ and ⊘. These new operations, which are inverses of basic interval operations + and ×, will be presented in the middle of this paper. Some numerical examples are given to illustrate the ability of proposed methods.

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A Unified Iterative Scheme for Solving Fully Fuzzy Linear System

Cited by 12 publications

References 11 publications

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

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

A New Approach for Solving Fully Fuzzy Linear Systems

An Application of Interval Arithmetic for Solving Fully Fuzzy Linear Systems with Trapezoidal Fuzzy Numbers

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