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Fuzzy linear matrix equation

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Abstract

The main aim of this paper is to discuss Fuzzy Linear Matrix Equations (shown as FLME) of the form AXB = C for finding its fuzzy solutions. In this paper, the parametric form of the fuzzy linear system is used. Necessary and sufficient conditions for the existence of the set of fuzzy solutions are derived, and a numerical procedure for calculating the solutions is designed.

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References

  • Abbasbandy S., Ezzati R., Jafarian A. (2006) LU decomposition method for solving fuzzy system of linear equations. Applied Mathematics and Computation 172: 633–643

    Article  MathSciNet  MATH  Google Scholar 

  • Allahviranloo T. (2003) Discussion: A comment on fuzzy linear systems. Fuzzy Sets and Systems 140: 559

    Article  MathSciNet  MATH  Google Scholar 

  • Allahviranloo T. (2004) Numerical methods for fuzzy system of linear equations. Applied Mathematics and Computation 155: 493–502

    Article  MathSciNet  MATH  Google Scholar 

  • Allahviranloo T. (2005a) Succesive over relaxation iterative method for fuzzy system of linear equations. Applied Mathematics and Computation 162: 189–196

    Article  MathSciNet  MATH  Google Scholar 

  • Allahviranloo T. (2005b) The Adomian decomposition method for fuzzy system of linear equations. Applied Mathematics and Computation 163: 553–563

    Article  MathSciNet  MATH  Google Scholar 

  • Allahviranloo T., Afshar Kermani M. (2006) Solution of a fuzzy system of linear equation. Applied Mathematics and Computation 175: 519–531

    Article  MathSciNet  MATH  Google Scholar 

  • Allahviranloo T., Ahmady E., Ahmady N., Shams Alketaby Kh. (2006) Block Jacobi two stage method with Gauss Sidel inner iterations for fuzzy systems of linear equations. Applied Mathematics and Computation 175: 1217–1228

    Article  MathSciNet  MATH  Google Scholar 

  • Asady B., Abasbandy S., Alavi M. (2005) Fuzzy general linear systems. Applied Mathematics and Computation 169: 34–40

    Article  MathSciNet  MATH  Google Scholar 

  • Dehghan M., Hashemi B. (2006) Iterative solution of fuzzy linear systems. Applied Mathematics and Computation 175: 645–674

    Article  MathSciNet  MATH  Google Scholar 

  • Friedman M., Ming M., Kandel A. (1998) Fuzzy linear systems. Fuzzy Sets and Systems 96: 201–209

    Article  MathSciNet  MATH  Google Scholar 

  • Friedman M., Ming M., Kandel A. (2003) Discussion: Author‘s reply. Fuzzy Sets and Systems 140: 561

    Article  MathSciNet  Google Scholar 

  • Goetschel R., Voxman W. (1986) Elementary calculus. Fuzzy Sets ans Systems 18: 31–43

    Article  MathSciNet  MATH  Google Scholar 

  • Kaleva O. (1987) Fuzzy differential equations. Fuzzy Sets and Systems 24: 301–317

    Article  MathSciNet  MATH  Google Scholar 

  • Lancaster P., Tismenetsky M. (1985) The theory of matrices. Academic Press, London

    MATH  Google Scholar 

  • Ma M., Friedman M., Kandel A. (2000) Duality in fuzzy linear systems. Fuzzy Sets and Systems 109: 55–58

    Article  MathSciNet  MATH  Google Scholar 

  • Navarra A., Odell P.L., Young D.M. (2001) A representation of general common solution to the matrix equations A 1 × B 1 =  C 1 and A 2 × B 2 = C 2 with applications. An International Journal of Computers and Mathematics with Applications 41: 929–935

    Article  MATH  Google Scholar 

  • Rao C.R., Mitra S.K. (1971) Generalized inverse of matrices and its applications. Wiley, New York

    MATH  Google Scholar 

  • Wang K., Zheng B. (2006) Inconsistent fuzzy linear systems. Applied Mathematics and Computations 181: 973–981

    Article  MathSciNet  MATH  Google Scholar 

  • Wanga X., Zhong Z., Ha M. (2001) Iteration algorithms for solving a system of fuzzy linear equations. Fuzzy Sets and Systems 119: 121–128

    Article  MathSciNet  Google Scholar 

  • Wu C.-X., Ma M. (1991) Embedding problem of fuzzy number space: Part I. Fuzzy Sets and Systems 44: 33–38

    Article  MathSciNet  MATH  Google Scholar 

  • Wu C.-X., Ma M. (1992) Embedding problem of fuzzy number space: Part III. Fuzzy Sets and Systems 46: 281–286

    Article  MathSciNet  MATH  Google Scholar 

  • Zheng B., Wang K. (2006) General fuzzy linear systems. Applied Mathematics and Computation 181: 1276–1286

    Article  MathSciNet  MATH  Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, Islamic Azad University, Science and Research Branch, Tehran, Iran

    T. Allahviranloo & M. Barkhordary

  2. Department of Mathematics, Islamic Azad University, Ardabil Branch, Ardabil, Iran

    N. Mikaeilvand

  3. Department of Mathematics, Islamic Azad University, Bandar Abbas Branch, Bandar Abbas, Iran

    M. Barkhordary

Authors
  1. T. Allahviranloo
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  2. N. Mikaeilvand
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  3. M. Barkhordary
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Correspondence to T. Allahviranloo.

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Allahviranloo, T., Mikaeilvand, N. & Barkhordary, M. Fuzzy linear matrix equation. Fuzzy Optim Decis Making 8, 165–177 (2009). https://doi.org/10.1007/s10700-009-9058-1

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  • DOI: https://doi.org/10.1007/s10700-009-9058-1

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