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System of type-2 fuzzy differential equations and its applications

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Abstract

This paper develops the mathematical framework and the solution of a system of type-2 fuzzy ordinary differential equations (T2FDE). The theory of T2FDEs is developed with type-2 fuzzy initial values, type-2 fuzzy boundary values and type-2 fuzzy parameters. Some natural phenomena can be modelled as dynamical systems whose initial conditions and/or parameters may be imprecise in nature. The imprecision of initial values and/or parameters is generally modelled by fuzzy sets. Here, the concept of generalized H2-differentiability, based on the extension of the class of differentiable type-2 fuzzy mappings or Hukuhara derivatives, is applied. Numerical simulations of type-2 fuzzy differential equations have also been developed. Several illustrative examples have been provided for different T2FDE models related to environmental dynamics and problems in mathematical biology.

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Authors and Affiliations

  1. Department of Mathematics, National Institute of Technology, Durgapur, 713209, India

    Abhirup Bandyopadhyay & Samarjit Kar

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  1. Abhirup Bandyopadhyay
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  2. Samarjit Kar
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Correspondence to Samarjit Kar.

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Bandyopadhyay, A., Kar, S. System of type-2 fuzzy differential equations and its applications. Neural Comput & Applic 31, 5563–5593 (2019). https://doi.org/10.1007/s00521-018-3380-x

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