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Type-2 fuzzy initial value problems under granular differentiability

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  • Mohapatra, Dhabaleswar
  • Chakraverty, S.

Abstract

This article investigates type-2 fuzzy initial value problems and introduces a novel strategy that capitalises on granular differentiability. Incorporating type-2 fuzzy numbers to depict the problem’s uncertainty may be advantageous from a practical standpoint. This work employs triangularly perfect quasi type-2 fuzzy numbers (TPQT2FNs) and defines the granular differentiability of TPQT2FN-valued functions. In addition, the solution approach for initial value problems with type-2 fuzzy initial conditions is discussed in the context of granular differentiability by transforming the type-2 fuzzy problem into a type-1 fuzzy problem using the lower membership function (LMF) and upper membership function (UMF) concepts. A couple of numerical examples are then examined to determine the applicability of the proposed method, and comparisons are made with existing type-2 fuzzy results and, in a special case, type-1 fuzzy results. In order to aid readers’ comprehension and study the behaviour of the numerical solution, three-dimensional graphical results are also shown.

Suggested Citation

  • Mohapatra, Dhabaleswar & Chakraverty, S., 2025. "Type-2 fuzzy initial value problems under granular differentiability," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 229(C), pages 435-447.
    • Handle: RePEc:eee:matcom:v:229:y:2025:i:c:p:435-447
    DOI: 10.1016/j.matcom.2024.10.002
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    References listed on IDEAS

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    1. Smita Tapaswini & S. Chakraverty, 2012. "A New Approach to Fuzzy Initial Value Problem by Improved Euler Method," Fuzzy Information and Engineering, Taylor & Francis Journals, vol. 4(3), pages 293-312, September.
    2. Mohapatra, Dhabaleswar & Chakraverty, S., 2023. "Initial value problems in Type-2 fuzzy environment," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 204(C), pages 230-242.
    3. M. Oberguggenberger & S. Pittschmann, 1999. "Differential Equations With Fuzzy Parameters," Mathematical and Computer Modelling of Dynamical Systems, Taylor & Francis Journals, vol. 5(3), pages 181-202, September.
    4. Smita Tapaswini & S. Chakraverty, 2012. "A new approach to fuzzy initial value problem by improved Euler method," Fuzzy Information and Engineering, Springer, vol. 4(3), pages 293-312, September.
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