Incremental three-way neighborhood approach for dynamic incomplete hybrid data

Abstract 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.