•To handle the uncertainty decision problems in incomplete hybrid data, a generalized three-way neighborhood decision model is proposed by distributing the interval-valued loss function to each object and averaging the interval-valued loss functions of all objects in the data-driven neighborhood class.•A matrix-based approach for representing three-way regions in the generalized three-way neighborhood decision model is presented by introducing the matrix forms of related concepts and the matrix operators.•An efficient framework for dynamically updating the three-way regions is provided when objects and attributes increase simultaneously.•An incremental algorithm based on matrix is designed for maintaining the three-way regions.•Experimental results demonstrate that the proposed incremental algorithm has an advantage in improving the computational performance. The theory of three-way decisions, as a powerful methodology of granular computing, has been widely used in making decision under uncertainty environments. Decision tasks in incomplete hybrid data including heterogeneous and missing features are of abundance in realistic situations. To deal with these tasks, some work based on three-way decisions has been investigated. However, the losses used for evaluating objects are precise real numbers, which makes these decision models have some limitations in applications when there exist missing values in incomplete hybrid data. Thus, this paper constructs a generalized three-way neighborhood decision model by assigning the interval-valued loss function to each object and further adopting an average strategy to integrate the interval-valued loss functions of objects in each data-driven neighborhood class. Moreover, considering that the objects and attributes of incomplete hybrid data will simultaneously change over time, this paper also provides an efficient framework to dynamically maintain three-way regions of the proposed model. An approach based on matrix to compute the three-way regions is first presented by introducing the matrix operations and the matrix forms of related concepts. Then, with the simultaneous variation of objects and attributes, the matrix-based incremental mechanism and algorithm are proposed for updating the three-way regions, respectively. Experimental results on nine datasets indicate that the proposed incremental algorithm can effectively improve the computational performance for evolving data in comparison with the static algorithm.