Repeatable random permutation set

Based on Dempster-Shafer evidence theory (DST), random permutation set (RPS) is proposed by replacing combinatorial number with permutation number and therefore incorporating order information. Besides, RPS could take DST as a special case when all items occur in the same order. However, the repetition of items is not allowed in RPS. To address this issue, we propose repeatable random permutation set (R2PS) 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 R2PS.