Solution for a System of First-Order Linear Fuzzy Boundary Value Problems

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S. Nagalakshmi, G. Suresh Kumar, B. Madhavi


In this paper, we consider homogeneous and non-homogeneous system of first order linear fuzzy boundary value problems (SFOLBVPs) under granular differentiability. Using the concept of horizontal membership function, we introduced the notion of first order granular differentiability for n-dimensional fuzzy functions. We present granular integral and its properties. Theorems on the existence and uniqueness of solutions for homogeneous and non-homogeneous SFOLFBVPs are proved. We develop an algorithm for solution of non-homogeneous SFOLBVPs under granular differentiability. We provide some examples to illustrate the validity of the proposed algorithm.

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  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. B. Bede, Mathematics of Fuzzy Sets and Fuzzy Logic, Springer, Berlin, Heidelberg, 2013.
  3. R. Boukezzoula, L. Jaulin, D. Coquin, A New Methodology for Solving Fuzzy Systems of Equations: Thick Fuzzy Sets Based Approach, Fuzzy Sets Syst. 435 (2022), 107–128.
  4. J.J. Buckley, T. Feuring, Y. Hayashi, Linear Systems of First Order Ordinary Differential Equations: Fuzzy Initial Conditions, Soft Comput. 6 (2002), 415–421.
  5. 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.
  6. N. Gasilov, S.E. Amrahov, A.G. Fatullayev, A Geometric Approach to Solve Fuzzy Linear Systems of Differential Equations, Appl. Math. Inform. Sci. 5 (2011), 484-499.
  7. M.S. Hashemi, J. Malekinagad, H.R. Marasi, Series Solution of the System of Fuzzy Differential Equations, Adv. Fuzzy Syst. 2012 (2012), 407647.
  8. 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.
  9. M. Mazandarani, N. Pariz, A.V. Kamyad, Granular Differentiability of Fuzzy-Number-Valued Functions, IEEE Trans. Fuzzy Syst. 26 (2018), 310–323.
  10. S. Prasad Mondal, N. Alam Khan, O. Abdul Razzaq, T. Kumar Roy, Adaptive Strategies for System of Fuzzy Differential Equation: Application of Arms Race Model, J. Math. Computer Sci. 18 (2018), 192–205.
  11. M. Najariyan, Y. Zhao, Granular Fuzzy PID Controller, Expert Syst. Appl. 167 (2021), 114182.
  12. M. Najariyan, N. Pariz, H. Vu, Fuzzy Linear Singular Differential Equations Under Granular Differentiability Concept, Fuzzy Sets Syst. 429 (2022), 169–187.
  13. L. Perko, Differential Equations and Dynamical Systems, Springer, New York, 2013.
  14. A. Piegat, M. Landowski, Solving Different Practical Granular Problems Under the Same System of Equations, Granul. Comput. 3 (2017), 39–48.
  15. 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, Granul. Comput. 7 (2021), 751–760.
  16. M.H. Suhhiem, R.I. Khwayyit, Semi Analytical Solution for Fuzzy Autonomous Differential Equations, Int. J. Anal. Appl. 20 (2022), 61.