Solution of the fully fuzzy linear systems using iterative techniques

Dehghan, Mehdi; Hashemi, Behnam; Ghatee, Mehdi

doi:10.1016/j.chaos.2006.03.085

Cited by 107 publications

(63 citation statements)

References 21 publications

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“…In the following simulations, we consider the specifications as follows: Where the exact solution is x = (1, 2, 2, 5) and y = (2,3,5,6 Table 1. Also, Figure 3 shows the convergence of the approximate solutions obtained from the proposed algorithm.…”

Section: Numerical Examplementioning

confidence: 99%

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Application of ANNs approach for solving fully fuzzy polynomials system

Novin¹,

Araghi²,

Amirfakhrian³

2017

Journal of Fuzzy Set Valued Analysis

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In processing indecisive or unclear information, the advantages of fuzzy logic and neurocomputing disciplines should be taken into account and combined by fuzzy neural networks. The current research intends to present a fuzzy modeling method using multi-layer fuzzy neural networks for solving a fully fuzzy polynomials system. To clarify the point, it is necessary to inform that a supervised gradient descent-based learning law is employed. The feasibility of the method is examined using computer simulations on a numerical example. The experimental results obtained from the investigation of the proposed method are valid and delivers very good approximation results.

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Section: Numerical Examplementioning

confidence: 99%

“…Further, Dubois and Prade [6] studied theoretical features of a fuzzy linear system . Iterative methods have been utilized to find the solution of fully fuzzy linear system by Dehgan et al [5]. The solutions to linear and nonlinear fuzzy systems were applied by [1,2,4].…”

Section: Introductionmentioning

confidence: 99%

Application of ANNs approach for solving fully fuzzy polynomials system

Novin¹,

Araghi²,

Amirfakhrian³

2017

Journal of Fuzzy Set Valued Analysis

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“…Proof Let A be an invertible matrix in (13). A row reduced echelon form of augmented (G | B) is employed to compute the solution.…”

Section: Are Equivalentmentioning

confidence: 99%

“…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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“…So many researchers have worked on FDEs find analytical and numerical solutions [1,2,3,4,6,7,8,9,10,11,12,13,16,18]. Finding error bound for the solution of FDEs is important task in application.…”

Section: Introductionmentioning

confidence: 99%

Error analysis for the solution of fuzzy differential equations using orthogonal basis functions

ghomi¹,

Shahsavari²,

Keshavarz³

2017

Communications on Advanced Computational Science with Applicati

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In this paper, the black pulse functions as a set of piecewise orthogonal functions are used to introduce a fuzzy solution for fuzzy differential equations. An error bound for the mentioned solution is investigated in details. To do this,1-cut for of the FDEs is considered and after finding the solution and other related equations, the fuzzy models and equations are introduce after allocating the spreads.

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Solution of the fully fuzzy linear systems using iterative techniques

Cited by 107 publications

References 21 publications

Application of ANNs approach for solving fully fuzzy polynomials system

Application of ANNs approach for solving fully fuzzy polynomials system

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

Error analysis for the solution of fuzzy differential equations using orthogonal basis functions

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