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.
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