In practical applications, there generally exist incomplete hybrid data with heterogeneous and missing features. The complex structures and the fast update of incomplete hybrid data bring a series of challenges for decision making in dynamic data environments. Three-way decisions, as an important cognitive method for analyzing uncertain problems, have been extensively applied into various fields. However, the existing studies rarely focus on exploring three-way decisions with incomplete hybrid information. To tackle this issue, we propose a Three-Way Neighborhood Decision Model (TWNDM) based on the data-driven neighborhood relation in terms of two pseudo-distance functions only satisfying the reflexivity. Considering that the addition and deletion of objects will result in the variation of information granules and decision structures, this paper presents a matrix-based dynamic framework for updating three-way regions (positive, boundary and negative regions) in TWNDM. A novel relation matrix is first constructed by using a pair of values to replace single value in the classical relation matrix. Then, the matrix-based approach for computing the three-way regions is established in the light of the new relation matrix, the decision matrix and the related induced matrices. Moreover, the matrix-based incremental mechanisms and algorithms for the maintenance of the three-way regions are presented when adding and removing objects, respectively. The results of comparative experiments demonstrate that the proposed incremental algorithms can improve the computational performance for maintaining three-way regions in TWNDM compared with the static algorithm.

在实际应用中，通常存在具有异构特征和缺失特征的不完整的混合数据。复杂的结构和不完整的混合数据的快速更新给动态数据环境中的决策带来了一系列挑战。三向决策作为一种分析不确定性问题的重要认知方法，已广泛应用于各个领域。但是，现有的研究很少集中于探索不完整的混合信息的三方决策。为了解决这个问题，我们提出了一种基于数据驱动的邻域关系的三路邻域决策模型（TWNDM），该模型基于两个仅满足反射性的伪距离函数。考虑到对象的添加和删除将导致信息粒度和决策结构的变化，本文提出了一种基于矩阵的动态框架，用于更新TWNDM中的三向区域（正向，边界和负向区域）。首先通过使用一对值替换经典关系矩阵中的单个值来构造一个新颖的关系矩阵。然后，根据新的关系矩阵，决策矩阵和相关的归纳矩阵，建立了基于矩阵的三向区域计算方法。此外，分别介绍了在添加和删除对象时用于维护三向区域的基于矩阵的增量机制和算法。比较实验结果表明，与静态算法相比，所提增量算法可以提高TWNDM中保持三向区域的计算性能。