Abstract: There are excessive and unorderly rules produced by traditional association rule mining, many of which are redundant. It is difficult for users to understand and use. To solve this problem, the relationship between the original rule-set and the rule-set representation was discussed and a new model was represented. The new model contained an inference system established with statistics to get minimum-redundant and lossless rule-set representation by getting rid of redundant rules. This minimum-redundant and lossless rules-set representation is more concise, more intelligible, and easier to manage and use. Especially, the rule-set is lossless so that it is able to switch to the original rule-set. It is so important because the switching keeps the completeness of rule-set representation. Experiments with four data sets show that the number of rules in the rule-set representation is reduced greatly.