Incremental updating probabilistic approximations under multi-level and multi-dimensional variations in hybrid incomplete decision systems

The data types of practical application systems are various (for example, Boolean, categorical, numerical, set-valued, interval-valued and incomplete, etc.), and such complex data systems exist widely in the real world; In addition, the data is dynamic in the process of collection and screening, not only the number of objects will change, but also the number of features will vary, which leads to the knowledge being constantly changed and needing to be updated with the collation process. In this paper, aiming at the dynamic change of data in the hybrid incomplete decision system (HIDS), we mainly focus on researching the incremental updating theory and method of probabilistic approximations under the multi-level and multi-dimensional variations of objects and attributes. Firstly, for the different binary relations of multiple data types in HIDS, a normalized combination relationship-based probabilistic rough set model is proposed. Next, multi-level and multi-dimensional variations (MLMDV) of objects and attributes are analyzed; for MLMDV of the object set and the attribute set in HIDS, dynamic knowledge updating mechanisms are researched, and a matrix-based incremental algorithm for updating probabilistic approximations is designed to avoid the repeated calculation of the static algorithm and improve efficiency. Finally, a series of experiments are conducted to evaluate the efficiency of the proposed method. The experimental results of 9 data sets show that the proposed incremental algorithm can effectively update the knowledge for the multi-level and multi-dimensional variants of objects and attributes, and is superior to the static knowledge acquisition method.