Random Walk in Random Permutation Set Theory
This work establishes a novel connection between RPST and random walk theory, potentially expanding RPST's applicability and improving problem-solving in uncertainty reasoning, though it appears incremental as it builds on existing frameworks.
The study tackled the problem of linking Random Permutation Set Theory (RPST) to random walk theory by constructing a random walk model based on RPST properties, revealing that it exhibits Gaussian-like characteristics and can be transformed into a Wiener process through scaling.
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.