Fuzzy support vector machines (FSVMs) are known for their excellent antinoise performance, but there is no general rule when the fuzzy membership function (FMF) is set up. A novel FSVM based on hyperbolas optimized by the quantum-inspired gravitational search algorithm (QGSH-FSVM) is proposed to handle this question. In the proposed QGSH-FSVM, the FMF is defined by two disparate hyperbolas, whose eccentricities are optimized by the quantum-inspired gravitational search algorithm. A variable called diversity, revealing the percentage of a sample in different classes, is proposed to distinguish outliers or noises from valid samples. Experimental results confirm that the QGSH-FSVM is able to provide the best solutions to different situations by optimizing its eccentricities. The traditional support vector machine and the FSVM based on affinity or the distance between a sample and its cluster center, however, can only succeed in some particular problems while failing in others.