Classification has applications in a wide range of fields including medicine, engineering, computer science and social sciences among others. In statistical terms, classification is inference about the unknown parameters, i.e., the true classes of future objects. Hence, various standard statistical approaches can be used, such as point estimators, confidence sets and decision theoretic approaches. For example, a classifier that classifies a future object as belonging to only one of several known classes is a point estimator. The purpose of this paper is to propose a confidence-set-based classifier that classifies a future object into a single class only when there is enough evidence to warrant this, and into several classes otherwise. By allowing classification of an object into possibly more than one class, this classifier guarantees a pre-specified proportion of correct classification among all future objects. An example is provided to illustrate the method, and a simulation study is included to highlight the desirable feature of the method.