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Solving Fuzzy Systems in Dual Form Using Wu’s Method

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Abstract

In this paper, fuzzy polynomial systems in dual form are considered and an algebraic approach for finding their solutions is presented. A dual fuzzy polynomial system in the form \(AX+B=CX+D \), where \(A, B, C,\) and \(D\) are fuzzy matrices, is converted to a system with real coefficients and variables first. Then, Wu’s algorithm is used as a solution procedure for solving this system. This algorithm leads to solving characteristic sets that are amenable to easy solution. Finally, the accuracy of the presented algorithm is shown via some examples.

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References

  1. Abbasbandy, S., Asady, B.: Newton’s method for solving fuzzy nonlinear equations. Appl. Math. Comput. 159(2), 349–356 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  2. Abbasbandy, S., Jafarian, A.: Steepest descent method for solving fuzzy nonlinear equations. Appl. Math. Comput. 174(1), 669–675 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  3. Abbasbandy, S., Otadi, M., Mosleh, M.: Minimal solution of general dual fuzzy linear systems. Chaos Solut. Fract. 37, 1113–1124 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  4. Abbasbandy, S., Otadi, M., Mosleh, M.: Numerical solution of a system of fuzzy polynomials by fuzzy neural network. Inf. Sci. 178(8), 1948–1960 (2008)

    Article  MATH  Google Scholar 

  5. Buckley, J., Feuring, T., Hayashi, Y.: Solving fuzzy equations using evolutionary algorithms and neural nets. Soft Comput. 6(2), 116–123 (2002)

    Article  MATH  Google Scholar 

  6. Cechlarova, K.: A note on unsolvable systems of max–min (fuzzy) equations. Linear Algebra Appl. 310, 123–128 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  7. Chou, S., Gao, X., McPhee, N.: A Combination of Ritt-Wu’s Method and Collins’ Method. Technical report, Austin, Texax, USA (1989)

    Google Scholar 

  8. Cox, D., Little, J., O’Shea, D.: Ideals, Varieties, and Algorithms : An Introduction To computational Algebraic Geometry and Commutative Algebra. Undergraduate Texts in Mathematics. Springer, New York (2007)

    Book  Google Scholar 

  9. Gao, X., Hou, X., Tang, J., Cheng, H.: Complete solution classification for the perspective-three-point problem. IEEE Trans. Pattern Anal. Mach. Intell. 25(8), 930–943 (2003)

    Article  Google Scholar 

  10. Goetschel, R., Voxman, W.: Elementary fuzzy calculus. Fuzzy Sets Syst. 18(1), 31–43 (1986)

    Article  MATH  MathSciNet  Google Scholar 

  11. Gong, Z., Guo, X., Liu, K.: Approximate solution of dual fuzzy matrix equations. Inf. Sci. 266, 112–133 (2014)

    Article  MathSciNet  Google Scholar 

  12. Jafarian, A., Measoomy, S.: Nia: on the solution of nonlinear fuzzy equations system by fuzzy neural networks method. Int. J. Fuzzy Syst. 15(3), 376–380 (2013)

    Google Scholar 

  13. Jin, M., Li, X., Wang, D.: A new algorithmic scheme for computing characteristic sets. J. Symb. Comput. 50, 431–449 (2013)

    Article  MATH  MathSciNet  Google Scholar 

  14. Tavassoli Kajani, M., Asady, B., Hadi-Vencheh, A.: An iterative method for solving dual fuzzy nonlinear equations. Appl. Math. Comput. 167(1), 316–323 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  15. Lee, K.H.: First Course Fuzzy Theory Applications. Advances in intelligent and soft computing. Springer, Berlin (2005)

    MATH  Google Scholar 

  16. Liang, L.R., Lu, S., Wang, X., Lu, Y., Mandal, V., Patacsil, D., Kumar, D.: Fm-test: a fuzzy-set-theory-based approach to differential gene expression data analysis. BMC Bioinform 7(S–4), S7 (2006)

    Article  Google Scholar 

  17. Ming, M., Friedman, M., Kandel, A.: Duality in fuzzy linear systems. Fuzzy Sets Syst 109, 55–58 (2000)

    Article  MATH  Google Scholar 

  18. Abbasi Molai, A., Basiri, A., Rahmany, S.: Resolution of a system of fuzzy polynomial equations using the gröbner basis. Inf. Sci. 220, 541–558 (2013)

    Article  MATH  MathSciNet  Google Scholar 

  19. Mosleh, M., Otadi, M., Abbasbandy, S.: Solution of fully fuzzy linear systems by st method. J Appl Math 8, 23–31 (2011)

    Google Scholar 

  20. Otadi, M., Mosleh, M.: Solution of fuzzy polynomial equations by modified adomain decomposition method. Soft Comput 15, 187–192 (2011)

    Article  MATH  Google Scholar 

  21. Salahshour, S., Homayoun Nejad, M.: Approximating solution of fully fuzzy linear systems in dual form. Int. J. Ind. Math. 5(1), 19–23 (2013)

    Google Scholar 

  22. Wen-tsun, W.: Basic principles of mechanical theorem proving in geometrics. J. Sys. Sci. Math. 4(3), 207–235 (1984)

    Google Scholar 

  23. Wen-Tsun, W.: On the decision problem and the mechanization of theorem-proving in elementary geometry. Contemp. Math. 29, 213–234 (1984)

    Google Scholar 

  24. Wen-tsun, W.: Mathematics Mechanization: Mechanical Geometry Theorem-Proving, Mechanical Geometry Problem-Solving and Polynomial Equations-Solving. Mathematics and Its Applications. BeijingbScience Press, London (2001). (This is an updated revised translation of the original Chinese work of the same title, Science Press, c2000)

  25. Wen-Tsun, W., Gao, X.: Mathematics mechanization and applications after thirty years. Front. Comput. Sci. China 1(1), 1–8 (2007)

    Article  Google Scholar 

  26. Wen-Tsun, W., Gao, X.S.: Automated reasoning and equation solving with the characteristic set method. J. Comput. Sci. Technol. 21(5), 756–764 (2006)

    Article  Google Scholar 

  27. Yeh, Ch-T: Reduction of fuzzy linear systems of dual equations. Int. J. Fuzzy Syst. 9(3), 173–178 (2007)

    MathSciNet  Google Scholar 

  28. Zadeh, L.A.: Fuzzy sets. Inf Control 8, 338–353 (1965)

    Article  MATH  MathSciNet  Google Scholar 

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Acknowledgments

The authors would like to thank Ali Abbasi Molai, Xiao-Shan Gao, and Donming Wang for their helpful discussions.

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Authors and Affiliations

  1. School of Mathematics and Computer Science, Damghan University, Damghan, Iran

    Marziyeh Boroujeni, Abdolali Basiri & Sajjad Rahmany

  2. Sorbonne Universités, UPMC Univ Paris 06, UMR 7606, LIP6 and LSTA, 75005, Paris, France

    Annick Valibouze

  3. CNRS, UMR 7606, LIP6, 75005, Paris, France

    Annick Valibouze

Authors
  1. Marziyeh Boroujeni
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  2. Abdolali Basiri
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  3. Sajjad Rahmany
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  4. Annick Valibouze
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Correspondence to Abdolali Basiri.

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Boroujeni, M., Basiri, A., Rahmany, S. et al. Solving Fuzzy Systems in Dual Form Using Wu’s Method. Int. J. Fuzzy Syst. 17, 170–180 (2015). https://doi.org/10.1007/s40815-015-0033-4

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  • DOI: https://doi.org/10.1007/s40815-015-0033-4

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