928
Views
5
CrossRef citations to date
0
Altmetric
Research Article

Highly efficient numerical scheme for solving fuzzy system of linear and non-linear equations with application in differential equations

ORCID Icon, ORCID Icon, ORCID Icon, ORCID Icon & ORCID Icon
Pages 777-810 | Received 13 Jun 2022, Accepted 08 Nov 2022, Published online: 22 Nov 2022

References

  • Zadeh LA. Fuzzy sets. Inf Control. 1965;8:338–353.
  • Zadeh LA. The concept of a linguistic variable and its application to approximation reasoning. Inf Sci. 1975;3:199–249.
  • Dubois D, Prade H. Operations on fuzzy numbers. J Syst Sci. 1978;9:613–626.
  • Dubois D, Prade H. Fuzzy sets and systems: theory and application. New York: Academic Press; 1980.
  • Mizumoto M, Tanaka K. The four operations of arithmetic on fuzzy numbers. Syst Comput Controls. 1976;7(5):73–81.
  • Mizumoto M, Tanaka K. Some properties of fuzzy numbers. In: Gupta MM, Ragade RK, Yager RR, editors. Advances in fuzzy Set theory and applications. Amsterdam: North-Holland; 1979. p. 156–164.
  • Chang SSL, Zadeh LA. On fuzzy mapping and control. IEEE Trans Syst Man Cybern. 1972;2:30–34.
  • Nahmias S. Fuzzy variables. Fuzzy Sets Syst. 1978;12:97–111.
  • Goetschel R, Voxman W. Elementary calculus. Fuzzy Sets Syst. 1986;18:31–43.
  • Moghadam KG, Ghanbari R, Amiri NM. Duality in bipolar triangular fuzzy number quadratic programming problems. In Proceedings of the International Conference on Intelligent Sustainable Systems, Palladam, Tirupur, India, 7–8 December 2017; pp. 1236–1238.
  • Congxin W, Ming M. On embedding problem of fuzzy number spaces. Fuzzy Sets Syst. 1991;44:33–38.
  • Puri ML, Ralescu D. Differential for fuzzy function. J Math Anal Appl. 1983;91:552–558.
  • Keyanpour M, Akbarian T. Solving intuitionistic Fuzzy nonlinear equations. J Fuzzy Set Value Anal. 2014;2014:1–6.
  • Buckley JJ, Qu Y. Solving linear and quadratic fuzzy equation. Fuzzy Sets Syst. 1990;38:43–59.
  • Buckley JJ, Qu Y. On using a-cuts to evaluate equations. Fuzzy Sets Syst. 1990;38:309–312.
  • Buckley JJ, Qu Y. Solving fuzzy equations: a new solution concept. Fuzzy Sets Syst. 1991;39:291–301.
  • Buckley JJ, Qu Y. Solving systems of linear fuzzy equations. Fuzzy Sets Syst. 1991;43:33–43.
  • Jajarmi A, Baleanu D, Zarghami KV, et al. A general fractional formulation and tracking control for immunogenic tumor dynamics. Math Methods Appl Sci. 2022;45(2):667–680.
  • Erturk VS, Godwe E, Baleanu D, et al. Novel fractional-order Lagrangian to describe motion of beam on nanowire. Acta Phys Pol A. 2021;140(3):265–272.
  • Jajarmi A, Baleanu D, Zarghami Vahid K, et al. A new and general fractional Lagrangian approach: a capacitor microphone case study. Results Phys. 2021;31:104950.
  • Baleanu D, Abadi MH, Jajarmi A, et al. A new comparative study on the general fractional model of COVID-19 with isolation and quarantine effects. Alexandria Eng J. 2022;61(6):4779–4791.
  • Kumar A, Malik M, Sajid M, et al. Existence of local and global solutions to fractional order fuzzy delay differential equation with non-instantaneous impulses. AIMS Math. 2022;7:2348–2369.
  • Khan MB, Srivastava HM, Mohammed PO, et al. Fuzzy-interval inequalities for generalized convex fuzzy-interval-valued functions via fuzzy Riemann integrals. AIMS Math. 2022;7:1507–1535.
  • Abbasbandy S, Ezzati R. Newton's method for solving system of fuzzy non-linear equations. Appl Math Comput. 2006;175(2):1189–1199.
  • Allahviranloo T, Asari S. Numerical solution of fuzzy polynomial by Newton-Raphson method. J Appl Math Islam Azad Univ Lahijan. 2011;7(4 (27)):17–44.
  • Mosleh M. Solution of dual fuzzy polynomial equations by modified Adomian decomposition method. Fuzzy Inf Eng. 2013;5:45–56.
  • Koam A, Akram M, Muhammad G, et al. LU decomposition scheme for solving m-Polar Fuzzy system of linear equations. Math Probl Eng. 2020;2020:1–19.
  • Akram M, Muhammad G, Koam ANA, et al. Iterative methods for solving a system of linear equation in bipolar fuzzy environment. Mathematics. 2019;7(728):1–25.
  • Sulaiman IM, Mamat M, Waziri MY, et al. Solving fuzzy nonlinear equation via levenberg-marquardt method. Far East J Math Sci. 2018;103:1547–1558.
  • Ma J, Feng G. An approach to H1 control of fuzzy dynamic systems. Fuzzy Sets Syst. 2003;137:367–386.
  • Cho YJ, Huang NJ, Kang SM. Nonlinear equations for fuzzy mapping in probabilistic normed spaces. Fuzzy Sets Syst. 2000;110:115–122.
  • Dennis JE, Schnabel RB. Numerical methods for unconstrained optimization and nonlinear equations. Hoboken, NJ: Prentice-Hall; 1983.
  • Fang J. On nonlinear equations for fuzzy mappings in probabilistic normed spaces. Fuzzy Sets Syst. 2002;131:357–364.
  • Shiri B, Irina P, Alijani Z. Classical approximation for fuzzy Fredholm integral equation. Fuzzy Sets Syst. 2021;404:159–177.
  • Zimmermann HJ. Fuzzy sets theory and its application. Dordrecht: Kluwer Academic Press; 1991.
  • Yao JS, Lin FT. Constructing a fuzzy flow-shop sequencing model based on statistical data. Int J Approximation Reason. 2002;29:215–234.
  • Rafiq N, Yaqoob N, Kausar N, et al. Computer-Based Fuzzy numerical method for solving engineering and Real-World Applications. Math Probl Eng. 2021;2021:1–13.
  • Mikaeilvand N, Noeiaghdam Z, Noeiaghdam S, et al. A novel technique to solve the fuzzy system of equations. Mathematics. 2020;8(5):850.
  • Saqib M, Akram M, Shahida B. Certain efficient iterative methods for bipolar fuzzy system of linear equations. J Intell Fuzzy Syst. 2020;39(3):1–15.
  • Akram M, Muhammad G, Allahviranloo T. Bipolar fuzzy linear system of equations. Comput Appl Math. 2019;38(69):1–29.
  • Akram S, Shams M, Rafiq N, et al. On the stability of Weierstrass type method with King's correction for finding all roots of non-linear function with engineering application. Appl Math Sci. 2020;14(10):461–473.
  • Qian G, Wang H, Feng X. Generalized hesitant fuzzy sets and their application in decision support system. Knowl Based Syst. 2013;37:357–365.
  • Rasham T, Shabbir MS, Agarwal P, et al. On a pair of fuzzy dominated mappings on closed ball in the multiplicative metric space with applications. Fuzzy Sets Syst. 2022;437:81–96.
  • Bataineh M, Alaroud M, Omari SA, et al. Series representations for uncertain fractional IVPs in the Fuzzy conformable fractional sense. Entropy . 2021;23(12):1646.