Solution and Analysis of Coupled Homogeneous Linear Intuitionistic Fuzzy Difference Equation

Subject Areas : Transactions on Fuzzy Sets and Systems

Abdul Alamin ¹ , Mostafijur Rahaman ² , Kamal Hossain Gazi ³ , Shariful Alam ⁴ , Sankar Prasad Mondal ^{5 *}

1 - Department of Applied Mathematics, Maulana Abul Kalam Azad University of Technology, Haringhata, Nadia-741249, West Bengal, India.
2 - Department of Mathematics, School of Liberal Arts & Sciences, Mohan Babu University, Tirupati, Andhra Pradesh 517102, India.
3 - Department of Applied Mathematics, Maulana Abul Kalam Azad University of Technology, Haringhata, Nadia-741249, West Bengal, India.
4 - Department of Mathematics, Indian Institute of Engineering Science and Technology, Howrah-711103, West Bengal, India.
5 - Department of Applied Mathematics, Maulana Abul Kalam Azad University of Technology, Haringhata, Nadia-741249, West Bengal, India.

Received: 2024-11-28 Accepted : 2025-02-01 Published : 2025-06-13

Keywords: Intuitionistic fuzzy set, Intuitionistic fuzzy difference equation, Stability analysis.,

Abstract :

In this paper, we have considered the initial valued coupled homogeneous linear difference equation in an intuitionistic fuzzy environment. We have given an outline of the general and analytical solutions at some fixed iteration levels and discussed the stability condition near the trivial intuitionistic equilibrium point of the system through a lemma. The proposed model is applied to check a predator-prey model and the graphical solutions are taken with taking different intuitionistic initial predator and prey population sizes to observe the dynamics in a short-sighted plan. Also, the graphical outcomes in an intuitionistic environment validate the theoretical result and the interrelated dynamical nature to fathom the significance of this work.

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