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Solution of the fully fuzzy linear systems using iterative techniques

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  • Dehghan, Mehdi
  • Hashemi, Behnam
  • Ghatee, Mehdi

Abstract

This paper mainly intends to discuss the iterative solution of fully fuzzy linear systems which we call FFLS. We employ Dubois and Prade’s approximate arithmetic operators on LR fuzzy numbers for finding a positive fuzzy vector x˜ which satisfies A∼x˜=b∼, where A∼ and b∼ are a fuzzy matrix and a fuzzy vector, respectively. Please note that the positivity assumption is not so restrictive in applied problems. We transform FFLS and propose 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 addition, the methods of Newton, quasi-Newton and conjugate gradient are proposed from nonlinear programming for solving a fully fuzzy linear system. Various numerical examples are also given to show the efficiency of the proposed schemes.

Suggested Citation

  • Dehghan, Mehdi & Hashemi, Behnam & Ghatee, Mehdi, 2007. "Solution of the fully fuzzy linear systems using iterative techniques," Chaos, Solitons & Fractals, Elsevier, vol. 34(2), pages 316-336.
    • Handle: RePEc:eee:chsofr:v:34:y:2007:i:2:p:316-336
    DOI: 10.1016/j.chaos.2006.03.085
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    1. Stefanini, Luciano & Sorini, Laerte & Guerra, Maria Letizia, 2006. "Simulation of fuzzy dynamical systems using the LU-representation of fuzzy numbers," Chaos, Solitons & Fractals, Elsevier, vol. 29(3), pages 638-652.
    2. El Naschie, M.S., 2005. "From experimental quantum optics to quantum gravity via a fuzzy Kähler manifold," Chaos, Solitons & Fractals, Elsevier, vol. 25(5), pages 969-977.
    3. Zhang, Hongbin & Liao, Xiaofeng & Yu, Juebang, 2005. "Fuzzy modeling and synchronization of hyperchaotic systems," Chaos, Solitons & Fractals, Elsevier, vol. 26(3), pages 835-843.
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    Cited by:

    1. Amit Kumar & Neetu & Abhinav Bansal, 2012. "A new computational method for solving fully fuzzy linear systems of triangular fuzzy numbers," Fuzzy Information and Engineering, Springer, vol. 4(1), pages 63-73, March.
    2. Liu, Shiang-Tai, 2009. "A revisit to quadratic programming with fuzzy parameters," Chaos, Solitons & Fractals, Elsevier, vol. 41(3), pages 1401-1407.
    3. Zhiyong Xiao & Zengtai Gong, 2022. "The Fuzzy Complex Linear Systems Based on a New Representation of Fuzzy Complex Numbers," Mathematics, MDPI, vol. 10(15), pages 1-14, August.

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