Iteration algorithms for solving a system of fuzzy linear equations

Wang, Xizhao; Zhong, Zimian; Ha, Ming-Hu

doi:10.1016/s0165-0114(98)00284-x

Cited by 61 publications

(28 citation statements)

References 6 publications

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“…In addition, some studies were dedicated to investigate different forms of FLSs. In (Wang et al 2001), solving FLS X = AX + U, where A is a crisp square matrix, and U a vector of fuzzy numbers was considered. A method for solving fuzzy linear systems of the form A 1 X + b 1 = A 2 X + b 2 -in which A 1 and A 2 are fuzzy square matrices, and b 1 and b 2 are fuzzy numbers vectors-was proposed in Muzzioli and Reynaerts (2006).…”

Section: Introductionmentioning

confidence: 99%

Type-2 fuzzy linear systems

2017

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Section: Introductionmentioning

confidence: 99%

Type-2 fuzzy linear systems

2017

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“…The research on fuzzy linear equations based on interval arithmetic and also, some researches on fuzzy linear systems can be seen in [8,9,10,11,12]. Many researchers have been studied on algebraic solutions methods of FPEs [5,6,7,13,14].…”

Section: Introductionmentioning

confidence: 99%

Minimal generalized solutions of fuzzy polynomial equations

Chehlabi¹

2015

Journal of Fuzzy Set Valued Analysis

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Fuzzy polynomial equations (FPEs) don't have algebraic solutions, generally. In this paper, we first, express and prove some relationships between Husdroof meter and length function on classes of triangular fuzzy numbers. We appraise the behavior of fuzzy polynomials by using the length function properties. Next, we transform a FPE into a generalized fuzzy polynomial equation (GFPE) and introduce generalized solutions and minimal generalized solutions concepts of FPEs. Finding minimal generalized solutions are discussed theoretically, in details. Finally, some numerical examples are given, illustrating our results.

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“…Wang et. al in [18], considered Jacobi and Gauss Seidel iteration methods for solving the fuzzy linear system. Summarised the structure of the paper is as follows:…”

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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Iteration algorithms for solving a system of fuzzy linear equations

Cited by 61 publications

References 6 publications

Type-2 fuzzy linear systems

Type-2 fuzzy linear systems

Minimal generalized solutions of fuzzy polynomial equations

On the global solution of a fuzzy linear system

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