The creation of the interestingness measures for evaluating the quality of the association rule - based knowledge plays an important role in the post-processing of the Knowledge Discovery from Databases. More and more interestingness measures are proposed by two approaches (subjective assessment and objective assessment), studying the properties or the attributes of the interestingness measures is important in understanding the nature of the objective interestingness measures. In this paper, we focus primarily on the objective interestingness measures to obtain a general view of recent researches on the nature of the objective interestingness measures, as well as complete a new classification on 109 selected objective interestingness measures on 6 criterions (independence, equilibrium, symmetry, variation, description, and statistics).