Random walk is an explainable approach for modeling natural processes at the
molecular level. The Random Permutation Set Theory (RPST) serves as a framework
for uncertainty reasoning, extending the applicability of Dempster-Shafer
Theory. Recent explorations indicate a promising link between RPST and random
walk. In this study, we conduct an analysis and construct a random walk model
based on the properties of RPST, with Monte Carlo simulations of such random
walk. Our findings reveal that the random walk generated through RPST exhibits
characteristics similar to those of a Gaussian random walk and can be
transformed into a Wiener process through a specific limiting scaling
procedure. This investigation establishes a novel connection between RPST and
random walk theory, thereby not only expanding the applicability of RPST, but
also demonstrating the potential for combining the strengths of both approaches
to improve problem-solving abilities.

通过在随机排列集合理论（RPST）的性质基础上构建随机行走模型，并进行蒙特卡罗模拟，我们发现通过 RPST 生成的随机行走表现出与高斯随机行走类似的特征，并可以通过特定的极限缩放过程转化为维纳过程，从而为 RPST 和随机行走理论建立了新的联系，扩展了 RPST 的适用性，并展示出结合这两种方法优势以改进问题解决能力的潜力。

随机排列集合论中的随机行走

Random Walk in Random Permutation Set Theory

Dempster rule of combination (DRC) is widely used for uncertainty reasoning
in intelligent information system, which is generalized to complex domain
recently. However, as the increase of identification framework elements, the
computational complexity of Dempster Rule of Combination increases
exponentially. To address this issue, we propose a novel quantum Dempster rule
of combination (QDRC) by means of Toffoli gate. The QDRC combination process is
completely implemented using quantum circuits.

提出了一种基于 Toffoli 门的量子 Dempster 组合规则 (QDRC)，用于智能信息系统中的不确定性推理，以缓解传统 Dempster 组合规则计算复杂度与识别框架元素增加之间的呈指数级增长的问题。