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Issue:On L^r-intuitionistic fuzzy Henstock–Kurzweil integral with application to intuitionistic fuzzy Laplace transform

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Title of paper: On Lr-intuitionistic fuzzy Henstock–Kurzweil integral with application to intuitionistic fuzzy Laplace transform
Author(s):
A. S. Wungreiphi     0009-0000-6775-9693
Department of Mathematics, Assam Don Bosco University, Tapesia Gardens, Kamarkuchi, Sonapur, Assam, India
wungreiphias@gmail.com
Fokrul Alom Mazarbhuiya     0000-0001-8364-8133
Department of Mathematics, Assam Don Bosco University, Tapesia Gardens, Kamarkuchi, Sonapur, Assam, India
fokrul.mazarbhuiya@dbuniversity.ac.in
Published in: Notes on Intuitionistic Fuzzy Sets, Volume 31 (2025), Number 3, pages 402–425
DOI: https://doi.org/10.7546/nifs.2025.31.3.402-425
Download:  PDF (300  Kb, File info)
Abstract: This article presents the concept of [math]\displaystyle{ L^r }[/math]-Henstock–Kurzweil integral of intuitionistic fuzzy number-valued function. First, we define the [math]\displaystyle{ L^r }[/math]-intuitionistic fuzzy Henstock–Kurzweil integral, explore its properties, demonstrate [math]\displaystyle{ L^r }[/math]-continuity of the primitive, and provide a convergence theorem. Furthermore, we show that this integral generalizes intuitionistic fuzzy Henstock–Kurzweil integral, has a broader scope and give a numerical example. We also introduce the proposed integral over an infinite interval and prove that the α- and β-cuts of the integral are Henstock–Kurzweil integrable. Finally, as an application, we define intuitionistic fuzzy Laplace transform based on [math]\displaystyle{ L^r }[/math]-intuitionistic fuzzy Henstock–Kurzweil integral and investigate the existence of intuitionistic fuzzy Laplace transform.
Keywords: Intuitionistic fuzzy set, [math]\displaystyle{ L^r }[/math]-intuitionistic fuzzy Henstock–Kurzweil integral, [math]\displaystyle{ L^r }[/math]-derivative, [math]\displaystyle{ L^r }[/math]-continuous, Intuitionistic fuzzy Laplace transform.
AMS Classification: 03F55, 26E50, 28E10.
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