  The twin support vector machine (TWSVM) classifier has attracted increasing
attention because of its low computational complexity. However, its performance
tends to degrade when samples are affected by noise. The granular-ball fuzzy
support vector machine (GBFSVM) classifier partly alleviates the adverse
effects of noise, but it relies solely on the distance between the
granular-ball's center and the class center to design the granular-ball
membership function. In this paper, we first introduce the granular-ball twin
support vector machine (GBTWSVM) classifier, which integrates granular-ball
computing (GBC) with the twin support vector machine (TWSVM) classifier. By
replacing traditional point inputs with granular-balls, we demonstrate how to
derive a pair of non-parallel hyperplanes for the GBTWSVM classifier by solving
a quadratic programming problem. Subsequently, we design the membership and
non-membership functions of granular-balls using Pythagorean fuzzy sets to
differentiate the contributions of granular-balls in various regions.
Additionally, we develop the granular-ball fuzzy twin support vector machine
(GBFTSVM) classifier by incorporating GBC with the fuzzy twin support vector
machine (FTSVM) classifier. We demonstrate how to derive a pair of non-parallel
hyperplanes for the GBFTSVM classifier by solving a quadratic programming
problem. We also design algorithms for the GBTSVM classifier and the GBFTSVM
classifier. Finally, the superior classification performance of the GBTWSVM
classifier and the GBFTSVM classifier on 20 benchmark datasets underscores
their scalability, efficiency, and robustness in tackling classification tasks.
