An Algorithm for the Solution of Second Order Linear Fuzzy System With Mechanical Applications

Article Sidebar

PDF
DOI: https://doi.org/10.28924/2291-8639-21-2023-76
Published: Jul 27, 2023
Cite as:
S. Nagalakshmi, G. Suresh Kumar, Ravi P. Agarwal, Chao Wang, An Algorithm for the Solution of Second Order Linear Fuzzy System With Mechanical Applications, Int. J. Anal. Appl., 21 (2023), 76.

Main Article Content

S. Nagalakshmi, G. Suresh Kumar, Ravi P. Agarwal, Chao Wang

Abstract

In this paper, we consider homogeneous and non-homogeneous second order linear fuzzy systems under granular differentiability. The concept of continuous n-dimensional fuzzy functions on the space of n-dimensional fuzzy numbers are introduced. Developed an algorithm for the solution of a non-homogeneous second order linear fuzzy system under granular differentiability. The proposed algorithm is applied to solve some well-known mechanical problems with fuzzy uncertainty.

Article Details

References

  1. Y. Barazandeh, B. Ghazanfari, Approximate Solution for Systems of Fuzzy Differential Equations by Variational Iteration Method, Punjab Univ. J. Math. 51 (2019), 13-33.
  2. R. Boukezzoula, L. Jaulin, D. Coquin, A New Methodology for Solving Fuzzy Systems of Equations: Thick Fuzzy Sets Based Approach, Fuzzy Sets Sys. 435 (2022), 107-128. https://doi.org/10.1016/j.fss.2021.06.003.
  3. O.S. Fard, N. Ghal-Eh, Numerical Solutions for Linear System of First-Order Fuzzy Differential Equations With Fuzzy Constant Coefficients, Inform. Sci. 181 (2011), 4765-4779. https://doi.org/10.1016/j.ins.2011.06.007.
  4. N. Gasilov, Sh. G. Amrahov, A.G. Fatullayev, A Geometric Approach to Solve Fuzzy Linear Systems of Differential Equations, Appl. Math. Inform. Sci. 5 (2011), 484-499. https://doi.org/10.48550/arXiv.0910.4307.
  5. M. Keshavarz, T. Allahviranloo, S. Abbasbandy, M.H. Modarressi, A Study of Fuzzy Methods for Solving System of Fuzzy Differential Equations, New Math. Nat. Comput. 17 (2021), 1-27. https://doi.org/10.1142/S1793005721500010.
  6. M. Mazandarani, N. Pariz, A.V. Kamyad, Granular Differentiability of Fuzzy-Number-Valued Functions, IEEE Trans. Fuzzy Syst. 26 (2017), 310-323. https://doi.org/10.1109/TFUZZ.2017.2659731.
  7. S.P. Mondal, N.A. Khan, O.A. Razzaq, S. Tudu, T.K. Roy, Adaptive Strategies for System of Fuzzy Differential Equation: Application of Arms Race Model, J. Math. Computer Sci. 18 (2018), 192-205. https://doi.org/10.22436/jmcs.018.02.07.
  8. S. Nagalakshmi, G.S. Kumar, B. Madavi, Solution for a System of First-Order Linear Fuzzy Boundary Value Problems, Int. J. Anal. Appl. 24 (2023), 4. https://doi.org/10.28924/2291-8639-21-2023-4.
  9. M. Najariyan, Yi. Zhao, The Explicit Solution of Fuzzy Singular Differential Equations Using Fuzzy Drazin Inverse Matrix, Soft Comput. 24 (2020), 11251–11264. https://doi.org/10.1007/s00500-020-05055-8.
  10. M. Najariyan, N. Pariz, H. Vu, Fuzzy Linear Singular Differential Equations Under Granular Differentiability Concept, Fuzzy Sets Syst. 429 (2022), 169-187. https://doi.org/10.1016/j.fss.2021.01.003.
  11. A. Piegat, M. Landowski, Solving Different Practical Granular Problems Under the Same System of Equations, Granular Comput. 3 (2018), 39-48. https://doi.org/10.1007/s41066-017-0054-5.
  12. A. Piegat, M. Pluciński, The Differences Between the Horizontal Membership Function Used in Multidimensional Fuzzy Arithmetic and the Inverse Membership Function Used in Gradual Arithmetic, Granular Comput. 7 (2022), 751-760. https://doi.org/10.1007/s41066-021-00293-z.
  13. C.H. Edwards, D.E. Penney, Differential Equations and Boundary Value Problems: Computing and Modeling, Fifth ed., Pearson Education, Boston, 2000.