Looking for associations in data is one of the data mining tasks that has aroused more interest in the literature. In this area, incorporating concepts of fuzzy set theory is useful in problems where imprecision and/or uncertainty appear. In most of the existing approaches, fuzzy association rules are widely seen as fuzzy rules, which are very different in nature from association rules, so problems like fuzzy inclusion and cardinality have been seldom taken into account explicitly, mostly providingad hocsolutions for capturing semantics. In contrast, in this study we have taken the more general and natural approach of considering the elements of the association rule mining framework and studying possible and sensible fuzzy extensions, referred here asfuzzy frameworks for mining associations. As fuzzy frameworks are abstract mathematical models, another key contribution of the article is the notion ofinterpretationsas mappings between fuzzy frameworks and specific datasets. This general analysis of the field is completed with a study of various important aspects that arise when proposing quality measures in a fuzzy environment, as well as those related to computational issues. The work also includes a review of the fuzzy framework that arises from fuzzy transactions regarded as fuzzy subsets of items, and shows that many of the approaches on fuzzy association rules that exist in the literature can be placed in the context of a proper interpretation of that framework.WIREs Data Mining Knowl Discov2016, 6:50–69. doi: 10.1002/widm.1176This article is categorized under:Fundamental Concepts of Data and Knowledge > Key Design Issues in Data MiningTechnologies > Association Rules