A stability-oriented virtual fuzzy soft set framework inspired by topological perspectives for decision analysis

Uncertainty-aware decision-making has attracted significant attention due to the complexity of real-world evaluation environments. Existing virtual logic-based approaches mainly address parameter-level uncertainty and do not explicitly capture instability arising from object evaluations and subjective perceptions. To overcome this limitation, this study proposes a novel Virtual Fuzzy Soft Set (VFSS) framework by integrating virtual logic with fuzzy soft set theory at the object level. The proposed model employs lower, central, and upper membership representations to characterise fuzziness, hesitation, and decision-maker reliability. A key contribution is the introduction of a stability measure, defined as the difference between upper and lower membership values, which quantifies inconsistency and cognitive uncertainty in subjective assessments. Based on this measure, a new decision-making algorithm is developed that jointly considers membership intensity and stability information, leading to more reliable and interpretable outcomes. The applicability of the framework is demonstrated through a case study on domestic tourism expenditures in Türkiye using quarterly data from the Turkish Statistical Institute (TÜİK) for 2020–2022. Results show that the VFSS-based approach provides stronger discrimination capability, improved robustness, and more effective uncertainty management than conventional fuzzy soft decision-making methods. The proposed framework offers a practical tool for decision analysis under uncertainty.