Legendre wavelets based approach for the solution of type-2 fuzzy uncertain smoking model of fractional order
ISSN: 0264-4401
Article publication date: 2 June 2023
Issue publication date: 15 June 2023
Abstract
Purpose
Investigation of the smoking model is important as it has a direct effect on human health. This paper focuses on the numerical analysis of the fractional order giving up smoking model. Nonetheless, due to observational or experimental errors, or any other circumstance, it may contain some incomplete information. Fuzzy sets can be used to deal with uncertainty. Yet, there may be some inconsistency in the membership as well. As a result, the primary goal of this proposed work is to numerically solve the model in a type-2 fuzzy environment.
Design/methodology/approach
Triangular perfect quasi type-2 fuzzy numbers (TPQT2FNs) are used to deal with the uncertainty in the model. In this work, concepts of r2-cut at r1-plane are used to model the problem's uncertain parameter. The Legendre wavelet method (LWM) is then utilised to solve the giving up smoking model in a type-2 fuzzy environment.
Findings
LWM has been effectively employed in conjunction with the r2-cut at r1-plane notion of type-2 fuzzy sets to solve the model. The LWM has the advantage of converting the non-linear fractional order model into a set of non-linear algebraic equations. LWM scheme solutions are found to be well agreed with RK4 scheme solutions. The existence and uniqueness of the model's solution have also been demonstrated.
Originality/value
To deal with the uncertainty, type-2 fuzzy numbers are used. The use of LWM in a type-2 fuzzy uncertain environment to achieve the model's required solutions is quite fascinating, and this is the key focus of this work.
Keywords
Acknowledgements
The first author would like to thank the University Grants Commission (UGC), New Delhi, for the financial assistance. Also, the authors would like to extend their heartfelt thanks to the reviewers for their time and effort in providing constructive feedback and helping to improve the quality of this work.
Citation
Mohapatra, D. and Chakraverty, S. (2023), "Legendre wavelets based approach for the solution of type-2 fuzzy uncertain smoking model of fractional order", Engineering Computations, Vol. 40 No. 4, pp. 868-920. https://doi.org/10.1108/EC-08-2022-0540
Publisher
:Emerald Publishing Limited
Copyright © 2023, Emerald Publishing Limited