Title: On periodic solutions of fuzzy max-type difference equation

Authors: Aasma Shabbir; Abdul Khaliq; Muhammad Shabbir; Lubna Mustafa

Addresses: Department of Mathematics, Riphah International University, Lahore, Pakistan ' Department of Mathematics, Riphah International University, Lahore, Pakistan ' Department of Mathematics, University of Engineering and Technology, Lahore, Pakistan ' Department of Mathematics, Virtual University of Pakistan, Lahore, Pakistan

Abstract: In this study, we examine the dynamical behaviour of positive solutions for the max-type fuzzy difference equation system: μ_n+1 = max{ψ/μ_n, ψ/μ_n-1, ψ/μ_n-2, μ_n-3}, n = 0, 1, 2, ..., where μ_n is a sequence of positive fuzzy numbers, and the parameter ψ and initial conditions μ_i, i = -3, -2, -1, 0 are positive fuzzy numbers. First, fuzzy set theory is applied to convert the fuzzy difference equation into ordinary difference equations with parameters. The periodic solution of the ordinary difference equations is derived using inequality techniques, mathematical induction, and iteration. Moreover, it is demonstrated that the solutions of fuzzy difference equation are persistence and bounded.

Keywords: fuzzy difference equation; fuzzy numbers; boundedness.

DOI: 10.1504/IJANS.2025.148932

International Journal of Applied Nonlinear Science, 2025 Vol.5 No.1, pp.57 - 86

Received: 12 Oct 2023
Accepted: 04 Feb 2025
Published online: 04 Oct 2025 *

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