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Data mining is an important technology to reveal the patterns from crime data. Although there are many researches about this topic, less work models the relations between rates of different kinds of crime. In this paper, an algorithm based on fuzzy association rules (AR) mining is proposed to discover these relations. Two datasets, which are crimes in Chicago from 2012 to 2017 and crimes in NSW from 2008 to 2012, are used for case studies. At first, crime data is preprocessed, where every kind of crime occurring in every district during every month is counted. For a crime in a combination of district and month, the membership function, which is based on hypothesis testing, is designed to evaluate the degree to which its rate is high, normal or low, and the fuzzy transactional dataset is formed. A bridge between fuzzy transactional dataset and binary AR mining algorithm is built, so those mature tools of binary AR mining can be applied to generate fuzzy ARs. In the results of case studies, the strong relations between rates of different crime can be found. There are many interesting and surprise rules, which are worthy to be further studied by domain experts. [ABSTRACT FROM AUTHOR]