  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.
