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. References: Acharya, A., Mahata, A., Sil, N., Mahato, S., Mukherjee, S., Mahato, S. K., & Roy, B. (2023). A prey-refuge harvesting model using intuitionistic fuzzy sets. Decision Analytics Journal, 8, Article ID 100308. Ali, W., Shaheen, T., Haq, I. U., Toor, H. G., Alballa, T., & Khalifa, H. A. E.-W. (2023). A novel interval-valued decision theoretic rough set model with intuitionistic fuzzy numbers based on power aggregation operators and their application in medical diagnosis. Mathematics, 11(19), Article ID 4153. Allahviranloo, T., & Ahmadi, M. B. (2010). Fuzzy Laplace transforms. Soft Computing, 14, 235–243. Atanassov, K. T., Vassilev, P., & Tsvetkov, R. (2013). 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