Breast mass cancer remains a great challenge for developing advanced computer-aided diagnosis (CADx) systems, to assist medical professionals for the determination of benignancy or malignancy of masses. This paper presents a novel approach to building fuzzy rule-based CADx systems for mass classification of mammographic images, via the use of weighted fuzzy rule interpolation. It describes an integrated implementation of such a classification system that ensures interpretable classification of masses through firing the rules that match given observations, while having the capability of classifying unmatched observations through fuzzy rule interpolation (FRI). In particular, a feature weight-guided FRI scheme is exploited to enable such inference. The work is implemented through integrating feature weights with a popular scale and move transformation-based FRI, with the individual feature weights derived from feature selection as a preprocessing process. The efficacy of the proposed CADx system is systematically evaluated using two real-world mammographic image datasets, demonstrating its explicit interpretability and potential classification performance.