A method for solving linear difference equation in Gaussian fuzzy environments

Abstract

To deal the uncertainty involved in the modeling of discrete system, fuzzy difference equation is the most capable mathematical tool. The present study provides a new aspect to fuzzy difference equation in the light of Zadeh’s extension principle. The uncertainty carrying by the initial condition and the coefficient of the homogeneous fuzzy difference equation is depicted in this article by Gaussian fuzzy number. On parallel, the notion of Gaussian fuzzy number is also reformulated in the sense of the classification into symmetric and non-symmetric Gaussian fuzzy number with both of the general and parametric representations. The arithmetic operations of Gaussian fuzzy numbers are redefined using two different methods, namely the transmission of average (TA) method and extension principle (EP) method. The numerical section of this article presents a comparison with an existing literature on the fuzzy linear difference equation and establishes the current approach to be smarter over the existing on in sense of strong solution criteria. The theoretical proposal of this study is validated by an application on the uncertain discrete dynamical system describing the gradual decay of species as an effect of climate change and other man-made occurrences in environments.

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Acknowledgements

The second author thinks that without the blessings of Shre Jai Jagannath the work can not be possible. The second author gratefully acknowledges the support of the University of Tabuk, Ministry of Education in Saudi Arabia.

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Correspondence to Sankar Prasad Mondal.

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Rahaman, M., Mondal, S.P., Algehyne, E.A. et al. A method for solving linear difference equation in Gaussian fuzzy environments. Granul. Comput. (2021). https://doi.org/10.1007/s41066-020-00251-1

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Keywords

  • Gaussian fuzzy number
  • Fuzzy difference equation
  • Extension principle method
  • Transmission average method