In the context of image classification, Concept Bottleneck Models (CBMs) first embed images into a set of human-understandable concepts, followed by an intrinsically interpretable classifier that predicts labels based on these intermediate representations. While CBMs offer a semantically meaningful and interpretable classification pipeline, they often sacrifice predictive performance compared to end-to-end convolutional neural networks. Moreover, the propagation of uncertainty from concept predictions to final label decisions remains underexplored. In this paper, we propose a novel uncertainty-aware and interpretable classifier for the second stage of CBMs. Our method learns a set of binary class-level concept prototypes and uses the distances between predicted concept vectors and each class prototype as both a classification score and a measure of uncertainty. These prototypes also serve as interpretable classification rules, indicating which concepts should be present in an image to justify a specific class prediction. The proposed framework enhances both interpretability and robustness by enabling conformal prediction for uncertain or outlier inputs based on their deviation from the learned binary class-level concept prototypes.