Probabilistic transformation of basic probability assignment based on weighted visibility graph networks

Dempster-Shafer evidence theory (DSET) provides a powerful framework for uncertain reasoning, offering a theoretical basis for decision-making under ambiguity. However, its core representation, the basic probability assignment (BPA), cannot be directly applied to probabilistic decision-making, prompting the need for effective probability transformation methods. A key challenge lies in quantifying the uncertainty inherent in BPAs to guide this transformation process. To address this, we propose an improved probabilistic transformation method that integrates belief entropy and weighted visibility graph networks, which yields more accurate and interpretable probability distributions than existing approaches. Specifically, given a frame of discernment and mass function, we first apply two refined belief entropy measures to evaluate the informational content of each focal element. Based on these entropy-derived orderings, we construct a weighted visibility graph that captures the structural relationships among focal elements. The weights from this graph are then used to compute a proportional belief transformation. Experimental validation across benchmark cases on classical BPA scenarios demonstrates that our method outperforms traditional approaches in terms of entropy consistency and decision quality, as evidenced by lower Kullback–Leibler (KL) divergence, higher probability information capacity (PIC), and reduced Shannon entropy. These results highlight the method's dual advantage in balancing decisiveness (via PIC maximization) and fidelity (via entropy minimization), making it a robust tool for uncertainty-aware decision support systems.