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

This article presents the concept of L^r-Henstock–Kurzweil integral of intuitionistic fuzzy number-valued function. First, we define the L^r-intuitionistic fuzzy Henstock–Kurzweil integral, explore its properties, demonstrate L^r-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 L^r-intuitionistic fuzzy Henstock–Kurzweil integral and investigate the existence of intuitionistic fuzzy Laplace transform.