A PROBID Hybrid Decision Model Based on Multi-Valued Neutrosophic Sets and Contact Numbers Integration

Multiple attribute decision making (MADM) is a vital part of modern decision science and often faces challenges in representing fuzzy information and maintaining dynamic adaptability under complex uncertain conditions. Although existing studies seek to improve heterogeneous information fusion using fuzzy set theory, research gaps persist in dynamic fuzzy decision mechanisms, reduction of subjective factors, and validation in multi-dimensional scenarios. The classic PROBID method, leveraging an ideal-average distance mechanism, has demonstrated considerable effectiveness across various domains. Yet, its strong sensitivity to attribute weight changes and limited adaptability in static contexts restrict broader applicability. To overcome these issues, this research proposes a hybrid model named multivalued neutrosophic contact numbers-based PROBID (MVCN-PROBID). By integrating the ternary semantic representation of multi-valued neutrosophic numbers (MVNNs) with the identity, discrepancy, and contrary theoretical mechanisms of contact numbers (CNs) in set pair analysis (SPA), a dual-dimensional dynamic evaluation system is established. This synergy within the PROBID framework partially alleviates traditional decision-making bottlenecks in dynamic fuzzy environments. Empirical analysis using two cases, agricultural drone procurement and investment firm selection, shows that MVCN-PROBID produces priority rankings closely matching practical needs. Internal robustness was examined via systematic parameter adjustments, and consistency was verified through multi-method comparative ranking, confirming the model's advantages in stability, applicability, and reliability. This work extends the PROBID method’s theoretical boundaries under a fuzzy mathematics framework, offering a structured solution for MADM in complex settings.