Inversion of the Radon transform is investigated by proposing a discrete formulation of the reconstruction problem via a fuzzy partition with Ruspini condition and the corresponding basic functions. Since the resulting systems of linear equations are gen-erally large scaled, sparse and ill-posed in practice, some algebraic iterative methods are considered for the solution of the discrete reconstruction problem. The proposed method is implemented to demonstrate its efficiency and to analyze its semi-convergence by considering the effect of noisy data. The numerical results are compared with the ones of the traditional methods: the pixel-based algebraic iterative methods and the filtered backprojection method. (c) 2023 Elsevier B.V. All rights reserved.