Research Article
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New hybrid of Conjugate Gradient Technique for Solving Fuzzy Nonlinear Equations

Year 2021, Volume: 2 Issue: 1, 1 - 8, 15.06.2021

Hisham Mohammed Khalil K. Abbo

Abstract

In this paper, we suggest a new technique for numerical solution of fuzzy nonlinear equations in parametric form using a new Conjugate Gradient Technique. Table of the numerical solution is given to show the efficiency of the proposed technique and which is compared with classical algorithms such as (Fletcher and Reeves (FR), Polak and Ribiere (PRP), Fletcher (CD), and (KH)) techniques.

Keywords

conjugate gradient technique fuzzy parametric form fuzzy nonlinear equations numerical techniques optimization technique Fuzzy interval

References

  • S. S. L. Cheng and L. A. Zadeh, “On fuzzy mapping and control,” IEEE Trans. Syst. Man Cybern., vol. 2, pp. 30–34, 1972.
  • D. Dubois and H. Prade, “Operations on fuzzy numbers,” Int. J. Syst. Sci., vol. 9, no. 6, pp. 613–626, 1978.
  • M. Mizumoto, “Some properties of fuzzy numbers,” 1979.
  • S. Nahmias, “Fuzzy variables,” Fuzzy sets Syst., vol. 1, no. 2, pp. 97–110, 1978.
  • L. A. Zadeh, “The concept of a linguistic variable and its application to approximate reasoning—II,” Inf. Sci. (Ny)., vol. 8, no. 4, pp. 301–357, 1975.
  • Y. J. Cho, N. J. Huang, and S. M. Kang, “Nonlinear equations for fuzzy mappings in probabilistic normed spaces,” Fuzzy Sets Syst., vol. 110, no. 1, pp. 115–122, 2000.
  • J. Fang, “On nonlinear equations for fuzzy mappings in probabilistic normed spaces,” Fuzzy Sets Syst., vol. 131, no. 3, pp. 357–364, 2002.
  • J. Ma and G. Feng, “An approach to H∞ control of fuzzy dynamic systems,” Fuzzy Sets Syst., vol. 137, no. 3, pp. 367–386, 2003.
  • J. J. Buckley and Y. Qu, “Solving linear and quadratic fuzzy equations,” Fuzzy sets Syst., vol. 38, no. 1, pp. 43–59, 1990.
  • J. J. Buckley and Y. Qu, “Solving fuzzy equations: a new solution concept,” Fuzzy sets Syst., vol. 39, no. 3, pp. 291–301, 1991.
  • S. Abbasbandy and B. Asady, “Newton’s method for solving fuzzy nonlinear equations,” Appl. Math. Comput., vol. 159, no. 2, pp. 349–356, Dec. 2004, doi: 10.1016/j.amc.2003.10.048.
  • A. Mottaghi, R. Ezzati, and E. Khorram, “A new method for solving fuzzy linear programming problems based on the fuzzy linear complementary problem (FLCP),” Int. J. Fuzzy Syst., vol. 17, no. 2, pp. 236–245, 2015.
  • M. Y. Waziri and A. U. Moyi, “An alternative approach for solving dual fuzzy nonlinear equations,” Int. J. Fuzzy Syst., vol. 18, no. 1, pp. 103–107, 2016.
  • I. Mohammed Sulaiman, M. Mamat, M. Yusuf Waziri, and N. Shamsidah Amzeh, “Barzilai-Borwein gradient method for solving fuzzy nonlinear equations,” Int. J. Eng. Technol., vol. 7, no. 3.28, p. 80, 2018, doi: 10.14419/ijet.v7i3.28.20972.
  • M. Mamat, A. Ramli, and M. L. Abdullah, “Broyden’s method for solving fuzzy nonlinear equations,” Adv. Fuzzy Syst., 2010, doi: 10.1155/2010/763270.
  • S. Abbasbandy and A. Jafarian, “Steepest descent method for solving fuzzy nonlinear equations,” Appl. Math. Comput., vol. 174, no. 1, pp. 669–675, Mar. 2006, doi: 10.1016/j.amc.2005.04.092.
  • E. K. P. Chong and S. H. Zak, An introduction to optimization. John Wiley & Sons, 2004.
  • W. Sun and Y.-X. Yuan, Optimization theory and methods: nonlinear programming, vol. 1. Springer Science & Business Media, 2006.
  • D. J. Dubois, Fuzzy sets and systems: theory and applications, vol. 144. Academic press, 1980.
  • L. A. Zadeh, “Fuzzy sets,” Inf. Control, vol. 8, no. 3, pp. 338–353, 1965.
  • R. Goetschel Jr and W. Voxman, “Elementary fuzzy calculus,” Fuzzy sets Syst., vol. 18, no. 1, pp. 31–43, 1986.
  • R. Fletcher and C. M. Reeves, “Function minimization by conjugate gradients,” Comput. J., vol. 7, no. 2, pp. 149–154, 1964, doi: 10.1093/comjnl/7.2.149.
  • L. C. W. Dixon, “Conjugate gradient algorithms: quadratic termination without linear searches,” IMA J. Appl. Math., vol. 15, no. 1, pp. 9–18, 1975.
  • E. Polak and G. Ribiere, “Note sur la convergence de méthodes de directions conjuguées,” ESAIM Math. Model. Numer. Anal. Mathématique Anal. Numérique, vol. 3, no. R1, pp. 35–43, 1969.
  • Hisham M. Khudhur; Khalil K. Abbo, “A New Type of Conjugate Gradient Technique for Solving Fuzzy Nonlinear Algebraic Equations.”

Year 2021, Volume: 2 Issue: 1, 1 - 8, 15.06.2021

Hisham Mohammed Khalil K. Abbo

Abstract

References

  • S. S. L. Cheng and L. A. Zadeh, “On fuzzy mapping and control,” IEEE Trans. Syst. Man Cybern., vol. 2, pp. 30–34, 1972.
  • D. Dubois and H. Prade, “Operations on fuzzy numbers,” Int. J. Syst. Sci., vol. 9, no. 6, pp. 613–626, 1978.
  • M. Mizumoto, “Some properties of fuzzy numbers,” 1979.
  • S. Nahmias, “Fuzzy variables,” Fuzzy sets Syst., vol. 1, no. 2, pp. 97–110, 1978.
  • L. A. Zadeh, “The concept of a linguistic variable and its application to approximate reasoning—II,” Inf. Sci. (Ny)., vol. 8, no. 4, pp. 301–357, 1975.
  • Y. J. Cho, N. J. Huang, and S. M. Kang, “Nonlinear equations for fuzzy mappings in probabilistic normed spaces,” Fuzzy Sets Syst., vol. 110, no. 1, pp. 115–122, 2000.
  • J. Fang, “On nonlinear equations for fuzzy mappings in probabilistic normed spaces,” Fuzzy Sets Syst., vol. 131, no. 3, pp. 357–364, 2002.
  • J. Ma and G. Feng, “An approach to H∞ control of fuzzy dynamic systems,” Fuzzy Sets Syst., vol. 137, no. 3, pp. 367–386, 2003.
  • J. J. Buckley and Y. Qu, “Solving linear and quadratic fuzzy equations,” Fuzzy sets Syst., vol. 38, no. 1, pp. 43–59, 1990.
  • J. J. Buckley and Y. Qu, “Solving fuzzy equations: a new solution concept,” Fuzzy sets Syst., vol. 39, no. 3, pp. 291–301, 1991.
  • S. Abbasbandy and B. Asady, “Newton’s method for solving fuzzy nonlinear equations,” Appl. Math. Comput., vol. 159, no. 2, pp. 349–356, Dec. 2004, doi: 10.1016/j.amc.2003.10.048.
  • A. Mottaghi, R. Ezzati, and E. Khorram, “A new method for solving fuzzy linear programming problems based on the fuzzy linear complementary problem (FLCP),” Int. J. Fuzzy Syst., vol. 17, no. 2, pp. 236–245, 2015.
  • M. Y. Waziri and A. U. Moyi, “An alternative approach for solving dual fuzzy nonlinear equations,” Int. J. Fuzzy Syst., vol. 18, no. 1, pp. 103–107, 2016.
  • I. Mohammed Sulaiman, M. Mamat, M. Yusuf Waziri, and N. Shamsidah Amzeh, “Barzilai-Borwein gradient method for solving fuzzy nonlinear equations,” Int. J. Eng. Technol., vol. 7, no. 3.28, p. 80, 2018, doi: 10.14419/ijet.v7i3.28.20972.
  • M. Mamat, A. Ramli, and M. L. Abdullah, “Broyden’s method for solving fuzzy nonlinear equations,” Adv. Fuzzy Syst., 2010, doi: 10.1155/2010/763270.
  • S. Abbasbandy and A. Jafarian, “Steepest descent method for solving fuzzy nonlinear equations,” Appl. Math. Comput., vol. 174, no. 1, pp. 669–675, Mar. 2006, doi: 10.1016/j.amc.2005.04.092.
  • E. K. P. Chong and S. H. Zak, An introduction to optimization. John Wiley & Sons, 2004.
  • W. Sun and Y.-X. Yuan, Optimization theory and methods: nonlinear programming, vol. 1. Springer Science & Business Media, 2006.
  • D. J. Dubois, Fuzzy sets and systems: theory and applications, vol. 144. Academic press, 1980.
  • L. A. Zadeh, “Fuzzy sets,” Inf. Control, vol. 8, no. 3, pp. 338–353, 1965.
  • R. Goetschel Jr and W. Voxman, “Elementary fuzzy calculus,” Fuzzy sets Syst., vol. 18, no. 1, pp. 31–43, 1986.
  • R. Fletcher and C. M. Reeves, “Function minimization by conjugate gradients,” Comput. J., vol. 7, no. 2, pp. 149–154, 1964, doi: 10.1093/comjnl/7.2.149.
  • L. C. W. Dixon, “Conjugate gradient algorithms: quadratic termination without linear searches,” IMA J. Appl. Math., vol. 15, no. 1, pp. 9–18, 1975.
  • E. Polak and G. Ribiere, “Note sur la convergence de méthodes de directions conjuguées,” ESAIM Math. Model. Numer. Anal. Mathématique Anal. Numérique, vol. 3, no. R1, pp. 35–43, 1969.
  • Hisham M. Khudhur; Khalil K. Abbo, “A New Type of Conjugate Gradient Technique for Solving Fuzzy Nonlinear Algebraic Equations.”
There are 25 citations in total.

Details

Primary Language English
Subjects Software Testing, Verification and Validation
Journal Section Research Articles
Authors

Hisham Mohammed 0000-0001-7572-9283

Khalil K. Abbo 0000-0001-5858-625X

Publication Date June 15, 2021
Submission Date January 14, 2021
Published in Issue Year 2021 Volume: 2 Issue: 1

Cite

APA Mohammed, H., & Abbo, K. K. (2021). New hybrid of Conjugate Gradient Technique for Solving Fuzzy Nonlinear Equations. Journal of Soft Computing and Artificial Intelligence, 2(1), 1-8.
AMA Mohammed H, Abbo KK. New hybrid of Conjugate Gradient Technique for Solving Fuzzy Nonlinear Equations. JSCAI. June 2021;2(1):1-8.
Chicago Mohammed, Hisham, and Khalil K. Abbo. “New Hybrid of Conjugate Gradient Technique for Solving Fuzzy Nonlinear Equations”. Journal of Soft Computing and Artificial Intelligence 2, no. 1 (June 2021): 1-8.
EndNote Mohammed H, Abbo KK (June 1, 2021) New hybrid of Conjugate Gradient Technique for Solving Fuzzy Nonlinear Equations. Journal of Soft Computing and Artificial Intelligence 2 1 1–8.
IEEE H. Mohammed and K. K. Abbo, “New hybrid of Conjugate Gradient Technique for Solving Fuzzy Nonlinear Equations”, JSCAI, vol. 2, no. 1, pp. 1–8, 2021.
ISNAD Mohammed, Hisham - Abbo, Khalil K. “New Hybrid of Conjugate Gradient Technique for Solving Fuzzy Nonlinear Equations”. Journal of Soft Computing and Artificial Intelligence 2/1 (June 2021), 1-8.
JAMA Mohammed H, Abbo KK. New hybrid of Conjugate Gradient Technique for Solving Fuzzy Nonlinear Equations. JSCAI. 2021;2:1–8.
MLA Mohammed, Hisham and Khalil K. Abbo. “New Hybrid of Conjugate Gradient Technique for Solving Fuzzy Nonlinear Equations”. Journal of Soft Computing and Artificial Intelligence, vol. 2, no. 1, 2021, pp. 1-8.
Vancouver Mohammed H, Abbo KK. New hybrid of Conjugate Gradient Technique for Solving Fuzzy Nonlinear Equations. JSCAI. 2021;2(1):1-8.

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