GDR β CAS ‐ VIKOR : A Density‐Aware Relative Granular Covering Rough Framework for Multi‐Criteria Decision Analysis

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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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