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Homomorphic solution of fully fuzzy linear systems

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Abstract

In this paper, a fully fuzzy linear system (FFLS) is considered. By defuzzifying, the (n × n) FFLS can be replaced by three (n × n) crisp linear systems, and consequently its homomorphic solution in canonical trapezoidal form based on three (n × n) crisp linear solutions associated with three parameters, value, ambiguity, and fuzziness, is calculated.

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References

  1. S. Abbasbandy, R. Ezzati, and A. Jafarian, “LU decomposition method for solving a fuzzy system of linear equations,” Appl. Math. Comput., 172, 633–643 (2006).

    Article  MATH  MathSciNet  Google Scholar 

  2. S. Abbasbandy, A. Jafarian, and R. Ezzati, “Conjugate gradient method for a fuzzy symmetric-positive definite system of linear equations,” Appl. Math. Comput., 171, 1184–1191 (2005).

    Article  MATH  MathSciNet  Google Scholar 

  3. T. Allahviranloo, N. Ahmady, and E. Ahmady, “A method for solving Nth order fuzzy differential equations,” Inform. Sci., In press.

  4. T. Allahviranloo, “Numerical methods for a fuzzy system of linear equation,” Appl. Math. Comput., 155, 493–502 (2004).

    Article  MATH  MathSciNet  Google Scholar 

  5. T. Allahviranloo, “The Adomian decomposition method for a fuzzy system of linear equations,” Appl. Math. Comput., 163, 553–563 (2005).

    Article  MATH  MathSciNet  Google Scholar 

  6. T. Allahviranloo, “Successive overrelaxation iterative method for a fuzzy system of linear equations,” Appl. Math. Comput., 162, 189–196 (2005).

    Article  MATH  MathSciNet  Google Scholar 

  7. T. Allahviranloo, N. Ahmady, and E. Ahmady, “A method for solving N-th order fuzzy differential equations,” Inform. Sci., In press.

  8. B. Asady, S. Abbasbandy, and M. Alavi, “Fuzzy general linear systems,” Appl. Math. Comput., 169, 34–40 (2005).

    Article  MATH  MathSciNet  Google Scholar 

  9. J. Buckley and Y. Qu, “Solving systems of linear fuzzy equations,” Fuzzy Sets Syst., 33–43 (1991).

  10. M. Caldas and S. Jafari, “θ-Compact fuzzy topological spaces,” Chaos, Solitons, Fractals, 25, 229–232 (2005).

    Article  MATH  MathSciNet  Google Scholar 

  11. M. Dehghan, B. Hashemi, and M. Ghatee, “Solution of fully fuzzy linear systems using iterative techniques,” Chaos, Solitons, Fractals, in press.

  12. M. Dehghan and B. Hashemi, “Iterative solution of fuzzy linear systems,” Appl. Math. Comput., in press, doi:10.1016/j.amc.2005.07.033.

  13. M. Delgado, M. A. Vila, and W. Voxman, “A fuzziness measure for fuzzy number,” Applications, Fuzzy Sets Syst., 94, 205–216 (1998).

    Article  MATH  MathSciNet  Google Scholar 

  14. D. Dubois and H. Prade, “Operations on fuzzy numbers,” J. Systems Sci., 9, 613–626 (1978).

    Article  MATH  MathSciNet  Google Scholar 

  15. MS. Elnaschie, “A review of E-infinity theory and the mass spectrum of high-energy particle physics,” Chaos, Solitons, Fractals, 19, 209–236 (2004).

    Article  Google Scholar 

  16. MS. Elnaschie, “The concepts of E infinity: An elementary introduction to the Cantorian-fractal theory of quantum physics,” Chaos, Solitons, Fractals, 22, 495–511 (2004).

    Article  Google Scholar 

  17. MS. Elnaschie, “On a fuzzy Kãhler manifold which is consistent with the two-slit experiment,” Int. J. Nonlin. Sci. Numeric. Simul., 6, 95–98 (2005).

    Google Scholar 

  18. MS. Elnaschie, “Elementary number theory in superstrings, loop quantum mechanics, twistors and E-infinity high energy physics,” Chaos, Solitons, Fractals, 27, 297–330 (2006).

    Article  Google Scholar 

  19. MS. Elnaschie, “Superstrings, entropy and the elementary particles content of the standard model,” Chaos, Solitons, Fractals, 29, 48–54 (2006).

    Article  Google Scholar 

  20. G. Feng and G. Chen, “Adaptive control of discrete-time chaotic systems: a fuzzy control approach,” Chaos, Solitons, Fractals, 23, 459–467 (2005).

    Article  MATH  MathSciNet  Google Scholar 

  21. M. Friedman, Ma Ming, and A. Kandel, “Fuzzy linear systems,” Fuzzy Sets Syst., 96, 201–209 (1998).

    Article  MATH  MathSciNet  Google Scholar 

  22. M. Friedman, Ma Ming, and A. Kandel, “Duality in fuzzy linear systems,” Fuzzy Sets Syst., 109, 55–58 (2000).

    Article  MATH  Google Scholar 

  23. W. Jiang, Q. Guo-Dong, and D. Bin, “H ∞ Variable universe adaptive fuzzy control for chaotic system,” Chaos, Solitons, Fractals, 24, 1075–1086 (2005).

    Article  MATH  MathSciNet  Google Scholar 

  24. A. Kaufmann and M. M. Gupta, Introduction to Fuzzy Arithmetic, Van Nostrand Reinhold, New York (1985).

    MATH  Google Scholar 

  25. Ma Ming and A. Kandel, “Duality in fuzzy linear systems,” Fuzzy Sets Syst., 109, 55–58 (2000).

    Article  MATH  Google Scholar 

  26. S. Muzzioli and H. Reynaerts, “Fuzzy linear systems of the form A 1 x + b 1 = A 2 x + b 2,” Fuzzy Sets Syst., In press.

  27. K. Nozavi and B. Fazlpour B, “Some consequences of space-time fuzziness,” Chaos, Solitons, Fractals, in press.

  28. J. H. Park, “Intuitionistic fuzzy metric spaces,” Chaos Solitons, Fractals, 22, 1039–1046 (2004).

    Article  MATH  MathSciNet  Google Scholar 

  29. Y. Tanaka, Y. Mizuno, and T. Kado, “Chaotic dynamics in the Friedman equation,” Chaos, Solitons, Fractals, 24, 407–422 (2005).

    Article  MATH  Google Scholar 

  30. X. Wang, Z. Zhong, and M. Ha, “Iteration algorithms for solving a system of fuzzy linear equations,” Fuzzy Sets Syst., 119, 121–128 (2001).

    Article  MATH  MathSciNet  Google Scholar 

  31. L. A. Zadeh, “The concept of a linguistic variable and its application to approximate reasoning,” Inform. Sci., 8, 199–249 (1975).

    Article  MathSciNet  Google Scholar 

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Authors and Affiliations

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

    T. Allahviranloo, N. A. Kiani, M. Barkhordary & M. Mosleh

Authors
  1. T. Allahviranloo
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  2. N. A. Kiani
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  3. M. Barkhordary
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  4. M. Mosleh
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Correspondence to T. Allahviranloo.

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Allahviranloo, T., Kiani, N.A., Barkhordary, M. et al. Homomorphic solution of fully fuzzy linear systems. Comput Math Model 19, 282–291 (2008). https://doi.org/10.1007/s10598-008-9004-z

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