The data collected from the real world are diverse and include categorical data, numerical data, incomplete data and noisy data. In addition, many real data sets may dynamically vary, and dynamic data display characteristics with multi-dimensional variations. However, for mixed incomplete data systems, most of the existing incremental methods only work well with single-dimensional dynamic data sets and are not suitable for processing specific multi-dimensional variations of objects and attributes. In this paper, we focus on researching dynamic approaches to efficiently update three-way regions based on the simultaneous variations of the object set and the attribute set in an incomplete neighborhood decision system (INDS). First, considering the complexity of data, we utilize matrix approaches to calculate three-way regions of the INDS based on a proposed neighborhood tolerance relation. Then, under the simultaneous addition of the object set and the attribute set in the INDS, we research incremental mechanisms based on the matrix to obtain three-way regions from previous knowledge. Subsequently, an incremental algorithm for updating three-way regions is proposed when the object set and the attribute set are simultaneously added to the INDS. Finally, the results of a series of experiments and comparisons based on UCI data sets show that the performance of the proposed incremental algorithm is much better than that of the traditional static algorithm, the integrated single-dimensional incremental algorithm and the single-level combined incremental algorithm.