Diagnosis and prognosis of gear systems play an important role in modern manufacturing. While first-principle-based inverse analysis is subject to various limitations, data-driven approaches such as many machine learning techniques have shown great promise in recent years. Nevertheless, major challenges remain. Machine learning generally requires large amount of high-quality training data which may not be available for many industrial systems. In particular, while gear faults are continuous in nature and exhibit many different scenarios, in practical situations owing to the high cost in data acquisition especially for fault scenarios, only a small number of discrete classes of faults, i.e., fault types and severities, can be recorded and employed in training. As such, the neural networks trained will need to deal with unseen faults when they are actually implemented. To tackle this challenge, in this research, we develop a fuzzy classification approach capable of handling fault scenarios that are not included in the training dataset. Through the integration of a fuzzification procedure, this fuzzy neural network (FNN) can produce classification outcome with probability and confidence level. An unseen fault scenario will be classified into the nearest fault class with probability, effectively yielding the diagnosis result under limited data. While fault features in gear vibration signals are hidden and have complex nonlinear relations with respect to fault scenarios, it is found that the kernel principal component analysis (KPCA) can enable the FNN to facilitate the correlation of fault features. Systematic case studies using experimental data acquired from a lab-scale gear system are carried out to validate the new approach.