This paper introduces a new and novel deterministic technique for mining association rules from quantitative data tables and databases and show how to use these techniques to devise a fuzzy-inference based apriori algorithm for discovering associations. The algorithm is sound and efficient. It introduces a complexity level that is equivalent to the complexity of the algorithm proposed by Agrawal. It can serve as the basis for numerous deterministic and heuristic variants. The mining algorithm uses a continuous method that is based on itemset support for discovering quantitative association rules. Instead of the common intersection operator we use the fuzzy proximity (equivalence) of items to determine the support. We present an algorithm for deriving the “atomic” association and generalize the algorithm to handle composite associations. In addition, we present a method for refining the results. Furthermore, we analyze the close surroundings of the region where the association rule is valid and take care of the “gray area” where an association rule just tends to be valid.