Repeatable Random Permutation Set
This work addresses a specific issue in information representation for decision support systems, but it appears incremental as it extends an existing theory.
The authors tackled the limitation of random permutation set (RPS) by proposing repeatable random permutation set (R²PS) to allow item repetition, common in real-life scenarios, and demonstrated its effectiveness through a simulated decision support system application.
Random permutation set (RPS), as a recently proposed theory, enables powerful information representation by traversing all possible permutations. However, the repetition of items is not allowed in RPS while it is quite common in real life. To address this issue, we propose repeatable random permutation set ($\rm R^2PS$) which takes the repetition of items into consideration. The right and left junctional sum combination rules are proposed and their properties including consistency, pseudo-Matthew effect and associativity are researched. Based on these properties, a decision support system application is simulated to show the effectiveness of $\rm R^2PS$.