The discovery of new knowledge by mining medical databases is crucial in order to make an effective use of stored data, enhancing patient management tasks. One of the main objectives of data mining methods is to provide a clear and understandable description of patterns held in data. We introduce a new approach to find association rules among quantitative values in relational databases. The semantics of such rules are improved by introducing imprecise terms in both the antecedent and the consequent, as these terms are the most commonly used in human conversation and reasoning. The terms are modeled by means of fuzzy sets defined in the appropriate domains. However, the mining task is performed on the precise data. These "fuzzy association rules" are more informative than rules relating precise values. We also introduce a new measure of accuracy, based on Shortliffe and Buchanan's certainty factors [Shortliffe E, Buchanan B. Math Biosci 1975;23:351-79]. Also, the semantics of the usual measure of usefulness of an association rule, called support are discussed and some new criteria are introduced. Our new measures have been shown to be more understandable and appropriate than ordinary ones. Several experiments on large medical databases show that our new approach can provide useful knowledge with better semantics in this field.