article · Expert Systems
This research introduces a novel Granular Density-based Relative β-Covering Approximation Space (GDR β CAS) and integrates it with the VIKOR method to create a framework for multi-criteria decision analysis under uncertainty. The approach extends classical β-covering rough sets by incorporating local data distribution properties. It constructs relative β-covering neighbourhoods and uses new granular density and relative granular distance measures to capture adaptive relationships and local structural information. A reliability factor, combining approximation accuracy and granular density, characterises uncertainty and distribution-aware knowledge. This mechanism allows the approximation process to adapt to diverse granular environments, offering a richer representation of alternatives. The framework improves discrimination among closely competing alternatives by integrating local uncertainty and structural reliability into the VIKOR method. Its effectiveness was demonstrated through a healthcare sustainability assessment involving 16 European countries, with comparative and sensitivity analyses confirming its consistency, discriminative capability, robustness, and stability.
This research offers a more robust way to make complex decisions, especially when data is uncertain or varied. It helps to better distinguish between similar options, leading to more reliable outcomes in areas like healthcare sustainability. This is crucial for effective resource allocation and policy making, ensuring decisions are based on a comprehensive understanding of available information.
The GDR β CAS-VIKOR framework provides an effective and reliable decision-support tool for complex multi-criteria decision-making problems under uncertainty. It could be applied in various sectors requiring robust assessment and ranking of alternatives, such as healthcare policy, environmental management, or financial risk assessment. The framework has been demonstrated through a healthcare sustainability assessment, suggesting it is at an applied research stage, potentially near-market for specific decision-support software.
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ABSTRACT Healthcare sustainability assessment is a challenging multi‐criteria decision‐making (MCDM) problem due to uncertainty, heterogeneous data distributions and complex interactions among evaluation criteria. To solve these problems, a novel Granular Density‐based Relative β ‐Covering Approximation Space (GDR β CAS) is proposed and an integrated GDR β CAS‐VIKOR framework is constructed for decision analysis under uncertainty in this paper. The proposed method is an extension of the classical β ‐covering rough sets, which considers the local distribution properties in the approximation process. Specifically, relative β ‐covering neighbourhoods are constructed to capture adaptive granular relationships among alternatives, while novel granular density and relative granular distance measures are introduced to quantify local structural information. Furthermore, a reliability factor that integrates approximation accuracy and granular density is developed to simultaneously characterize uncertainty and distribution‐aware knowledge. This mechanism enables the approximation process to adapt to heterogeneous granular environments and provides a richer representation of alternatives than existing covering‐based rough set models. The resulting reliability information is incorporated into the VIKOR method, enabling the framework to consider not only criterion performance but also local uncertainty distribution and structural reliability, which improves discrimination among closely competing alternatives. The effectiveness of the proposed framework is demonstrated through a healthcare sustainability assessment involving 16 European countries. Comparative analyses with TOPSIS, VIKOR, COPRAS, MABAC and CODAS confirm the consistency and discriminative capability of the proposed approach, while sensitivity analyses with respect to , , and verify its robustness and stability. The results demonstrate that the GDR β CAS–VIKOR framework provides an effective and reliable decision‐support tool for complex MCDM problems under uncertainty.
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DOI: 10.1111/exsy.70412
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