Improved evidential three-way decisions in incomplete multi-scale information systems

Granular computing, by simulating human thought processes, provides a paradigm for solving complex decision-making problems. The three-way decision is a key component of granular computing. Compared to traditional decision-making methodologies, it introduces “deferred decision-making”, allowing for multi-granularity exploration of alternatives. This process gradually refines the granularity of alternatives, leading to a transition between acceptance and rejection. Moreover, data structures in the real world are typically multi-granular, multi-level, and incomplete. Compared to single-scale information systems, incomplete multi-scale information systems provide richer decision foundations by mapping information to different levels. Additionally, they allow for more precise and flexible decision-making by integrating attribute information from different levels at a specific granularity, depending on requirements. Therefore, this paper seeks to present a three-way multi-scale decision-making methodology under incomplete environments. First, an integration methodology under incomplete multi-scale information systems by using the best-worst method is built, which comprehensively considers the importance of each scale of attributes. Second, the grey relation analysis calculation is integrated into the technique for order preference by similarity to ideal solution methodology to obtain the score of alternatives, serving as the conditional probability of three-way decisions, which compensates for the problem of Euclidean distance failures due to the correlation among indicators. Third, according to the evidence theory and the enhanced belief Jensen-Sharma-Mittal divergence, the thresholds of three-way decisions are fused, improving the classification efficiency of three-way decisions for alternatives. Finally, the effectiveness of the methodology established in this paper is validated using the campus environment evaluation data set collected through the Questionnaire Star from Shanxi University, China.