Real-word applications often involve a binary hypothesis testing problem with one of the two hypotheses ill-defined and hard to be characterized precisely by a single measure. In this paper, we develop a framework that integrates multiple hypothesis testing measures into a unified decision basis, and apply kernel-based classification techniques, namely, Kernel Fisher Discriminant (KFD) and Support Vector Machine (SVM), to optimize the integration. Experiments conducted on speaker verification demonstrate the superiority of our approaches over the predominant approaches.