Due to the strict requirements of extremely high accuracy and fast computational speed, real-time transient stability assessment (TSA) has always been a tough problem in power system analysis. Fortunately, the development of artificial intelligence and big data technologies provide the new prospective methods to this issue, and there have been some successful trials on using intelligent method, such as support vector machine (SVM) method. However, the traditional SVM method cannot avoid false classification, and the interpretability of the results needs to be strengthened and clear. This paper proposes a new strategy to solve the shortcomings of traditional SVM, which can improve the interpretability of results, and avoid the problem of false alarms and missed alarms. In this strategy, two improved SVMs, which are called aggressive support vector machine (ASVM) and conservative support vector machine (CSVM), are proposed to improve the accuracy of the classification. And two improved SVMs can ensure the stability or instability of the power system in most cases. For the small amount of cases with undetermined stability, a new concept of grey region (GR) is built to measure the uncertainty of the results, and GR can assessment the instable probability of the power system. Cases studies on IEEE 39-bus system and realistic provincial power grid illustrate the effectiveness and practicability of the proposed strategy.