Learning relations of objects has recently emerged as a new promising trend for supervised machine learning. Case-based reasoning (CBR) is a subfield of machine learning, which attempts to solve new problems by reusing previous experiences. There is a close link between learning of relations and case-based reasoning in the sense that relation analysis between cases is a core task in a CBR procedure. Traditional CBR systems built upon similar relations can only use local information, and they are restricted by the similarity requirement, i.e., the availability of similar cases to new problems. This paper proposes a new CBR approach that exploits the information about dissimilar relations for solving new problems. A fuzzy dissimilarity model consisting of fuzzy rules has been developed for assessing dissimilarity between cases. Identifying dissimilar cases enables global utilization of more information from the case library and thereby contributes to the avoidance of the similarity constraint with a conventional CBR method. Empirical studies have demonstrated that fuzzy dissimilarity models can be built upon a small case library while still yielding competent performance of the CBR system.