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Granular Computing

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04-01-2021 | Original Paper

A method for solving linear difference equation in Gaussian fuzzy environments

Authors: Mostafijur Rahaman, Sankar Prasad Mondal, Ebrahem A. Algehyne, Amiya Biswas, Shariful Alam

Published in: Granular Computing | Issue 1/2022

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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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Title: A method for solving linear difference equation in Gaussian fuzzy environments
Authors: Mostafijur Rahaman
Sankar Prasad Mondal
Ebrahem A. Algehyne
Amiya Biswas
Shariful Alam
Publication date: 04-01-2021
Publisher: Springer International Publishing
Published in: Granular Computing / Issue 1/2022
Print ISSN: 2364-4966
Electronic ISSN: 2364-4974
DOI: https://doi.org/10.1007/s41066-020-00251-1

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