Association rule mining plays a very important role in the distributed environment for Big Data analysis. The massive volume of data creates imminent needs to design novel, parallel and incremental algorithms for the association rule mining in order to handle Big Data. In this paper, a framework is proposed for incremental parallel interesting association rule mining algorithm for Big Data. The proposed framework incorporates interestingness measures during the process of mining. The proposed framework works to process the incremental data, which usually comes at different times, the user's important knowledge is explored by processing of new data only, without having to return from scratch. One of the main features of this framework is to consider the user domain knowledge, which is monotonically increased. The model that incorporates the users’ belief during the extraction of patterns is attractive, effective and efficient. The proposed framework is implemented on public datasets as well as it is evaluated based on the interesting results that are found.