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International Journal of Neutrosophic Science
Volume 18 , Issue 4, PP: 16-43 , 2022 | Cite this article as | XML | Html |PDF

Title

Bipolar Trapezoidal Neutrosophic Differential Equation and its Application

Authors Names :   M. Lathamaheswari   1 *     S. Sudha   2  

1  Affiliation :  Department of Mathematics, Hindustan Institute of Technology & Science, Chennai-603 103, India.

    Email :  lathamax@gmail.com


2  Affiliation :  Department of Mathematics, Hindustan Institute of Technology & Science, Chennai-603 103, India;Department of Mathematics Mohamed Sathak AJ College of Engineering, Chennai-603103,India

    Email :  sudha.aarpitha@gmail.com



Doi   :   https://doi.org/10.54216/IJNS.180402

Received: February 24, 2022 Accepted: June 16, 2022

Abstract :

Neutrosophic set plays a vital role in dealing with indeterminacy in real-world problems. Differential equations represent the relation between a function and its derivatives and its applications have importance in both pedagogical and real life. In this paper, neutrosophic differential equation is proposed and solved using bipolar trapezoidal neutrosophic number and applied the concept in predicting bacterial reproduction over separate bodies with graphical representation using MATLAB. Also, comparative analysis is done with the existing method to prove the effectiveness of the proposed method.

Keywords :

Trapezoidal Neutrosophic Numbers; Neutrosophic Set; Neutrosophic Differential Equations; Bipolar Trapezoidal Neutrosophic Number; Neutrosophic Numbers.

References :

[1] Zadeh, L .A., Fuzzy Sets, Information and Control., 8,338-353,1965.

[2] Krassimir T. Atanassov. Intuitionistic Fuzzy sets and systems., 20(1) 87-96, 1986.

[3] Smarandache, F., A Unifying Field in Logics Neutrosophy: Neutrosophic probability, Set and Logic.

Rehoboth: American Research Press, (1998).DOI:10.5281/zenoda.49174.

[4] Smarandache. F., Neutrosophy and Neutrosophic Logic, Set, Probability, and Statistics University of New

Mexico, Gallup, NM87301, USA (2002).

[5] J.J. Buckley., T. Feuring., & Y. Hayashi., Linear systems of first order ordinary differential equations Fuzzy

initial conditions., Soft Computing-A Fusion of Foundations, Methodologies and Applications.6(6),415-421,

2002.

[6] D.S-Le, H.Vu, & P.D- Nguyen., The formulas of the solution for linear-order random fuzzy differential

Equations. Journal of Intelligent and Fuzzy Systems, 28,795-807,2015.

[7] Said Melliani., Razika Ettoussi, R., Mhamed Elomari., & Lalla Saadia Chadli., Solution of intuitionistic fuzzy

differential equation by successive approximations Method. Notes on Intuitionistic Fuzzy Sets, ISSN 1310-4926

Vol. 21(2), 51-62,2015.

[8] Abdelati EI Allaoui., Said Melliani., Youssef Allaoui., & Lalla Saadia Chali., Averaging of intuitionistic fuzzy

differential equations. Notes on Intuitionistic Fuzzy Sets, Vol. 23(2),44-54,2017.

[9] I. R.Sumathi, I. Mohana Priya, V., A New perspective on Neutrosophic Differential Equation. International

Journal of Engineering & Technology, 7(4.10), 422-425, 2018.

[10] Moi, S., Biswas, S., Pal, S., Neutrosophic Linear Differential Equations with a New Concept of Neutrosophic

Derivative. In: Smarandache, F., Abdel-Basset, M. (Eds). (2021). Neutrosophic Operational Research.

Springer,Cham.

[11] Sumathi, I. R., Antony Crispin Sweety, C., New approach on differential equation via trapezoidal

Neutrosophic number. Complex and Intelligent systems 5, 417-424,2019.

[12] Moi, S., Biswas, S. & Pal, S.. Second-order Neutrosophic boundary-value problems, Complex and

Intelligent Systems 7,1079-1098,2021.

[13] Deli, I., & Subas, Y., A ranking method of single valued neutrosophic numbers and its applications to multiattribute

decision making problems. International Journal of Machine Learning and Cybernetics.8,1309-

1322, 2017.

[14] T. Allahviranloo., M. Shafiee., & Y. Nejatbakhsh., A note on fuzzy differential equations and the

extension principle.,179(12),2049-2051, 2009.

[15] Marine Mizukoshi, M.T., Barros, L.C., Chalco-Cano, Y., Roman-Flores,H., & Bassanezi, R. C., Fuzzy

differential equations and the extension principle. Journal of information science, 177(17),3627-3635,2013.

[16] K. Ivaz, A. Khastan, Juan, J.Nieto., A Numerical Method for Fuzzy Differential Equations and Hybrid Fuzzy

Differential Equation, Abstract and Applied Analysis,Vol.2013.doi:10.1155/2013/735128.

[17] Yu, Wen., &Jafari, Raheleh, (Eds). (2019). Modeling and Control of Uncertain Nonlinear Systems with

Fuzzy Equations and Z-Numbers. Fuzzy Differential Equations: Wiley-IEEE Press.

[18] Mazandarani, M., & Xiu,L., A Review on Fuzzy Differential Equations. IEEE Access, 9,62195-

62211,2021.

[19] Melliani,Said., & Lalla Saadia Chadli., Intuitionistic fuzzy differential equations. Notes on Intuitionistic

Fuzzy Sets 6.2, 37-41, 2000.

[20] Wang., L ei., Guo, Sicong., New Results on Multiple Solutions for Intuitionistic Fuzzy Differential

Equations. Journal of Systems Science and Information, Vol 4(6), 560-573.

[21] Abdelati El Allaoui., & Lalla Sadia Chadli., The Existence and Uniqueness of Intuitionistic fuzzy Solution for

Intuitionistic Fuzzy Partial Functional Differential Equations. International Journal of Differential Equations, 1-

13, 2019.

[22] Omer Akin & Selami Bayeg., System of intuitionistic fuzzy differential equations with intutionistic fuzzy

initial values. Notes on Intuitionistic Fuzzy Sets, 2018.doi: 10.7546/nifs.2018.24.4.141-171.

[23] Castilo, O., Melin, P., & Kacprzyk, J. (Eds).(2020). Intutionistic and Type-2 Fuzzy Logic Enhancements in

Neural and Optimization Algorithms: Theory and Applications Volume 862. Doi: 10.10007/978-3-030-

35445-9.


Cite this Article as :
M. Lathamaheswari , S. Sudha, Bipolar Trapezoidal Neutrosophic Differential Equation and its Application, International Journal of Neutrosophic Science, Vol. 18 , No. 4 , (2022) : 16-43 (Doi   :  https://doi.org/10.54216/IJNS.180402)