Single-Valued Neutrosophic Pessimistic Multi-Granulation Rough Set Model Based on (<i>a</i>,<i>b</i>,<i>c</i>)-cut Relations and its Applications

To address uncertainty in multi-source data, this paper proposes a single-valued neutrosophic pessimistic multi-granulation rough set (P-SVN-MGRS) model based on (a,b,c)-cut relations. In this framework, each neutrosophic relation is characterized by three membership-degree functions: T(x,y), I(x,y), and F(x,y). These functions correspond to truth-membership, indeterminacy, and falsity, respectively. The (α,β,γ)-cut relation employs parameters α,β,γ∈(0,1] as thresholds for the three functions. A pair (x,y) belongs to the cut relation if and only if T(x,y)≥α, I(x,y)≤β, and F(x,y)≤γ. P-SVN-MGRS adopts a "pessimistic" strategy for conservative information aggregation. The lower approximation of a target set is defined as the intersection of lower approximations induced by each cut relation across all granulations. The upper approximation is the union of the corresponding upper approximations, ensuring cautious and robust decision-making under multi-source uncertainty. First, we verify via counterexamples that the posets formed by classical upper and lower rough approximation operators-induced by (a,b,c)-cut relations over serial single-valued neutrosophic relations-do not generally constitute lattice structures. Then, within the multi-granulation framework, we systematically construct the proposed pessimistic model and rigorously derive its key mathematical properties. Finally, we validate the model through a case study on college evaluation.Experimental results show that compared with the single-granulation neutrosophic rough set model, P-SVN-MGRS achieves significant improvements: precision increases by13.3%, recall rises by17.6%, and mean uncertainty decreases by34%. These findings suggest that P-SVN-MGRS significantly enhances decision stability. It provides a robust tool for complex decision-support systems, particularly in contexts requiring dynamic granularity adjustment and cautious aggregation under uncertainty.