Random Permutation Set

For exploring the meaning of power set in evidence theory, a possible explanation is proposed from view Pascal’s triangle and combinatorial number. Here comes question: what would happen if number replaced by permutation number? To address this issue, new kind set, named as random (RPS), paper, which consists event space (PES) mass function (PMF). The PES certain considers all that set. elements are called events. PMF describes chance happen. Based on PMF, RPS can be viewed permutation-based generalization finite Besides, right intersection (RI) left (LI) events presented. RI LI, orthogonal sum (ROS) (LOS) PMFs proposed. In addition, numerical examples shown to illustrate conceptions. comparisons probability discussed summarized. Moreover, an RPS-based data fusion algorithm applied threat assessment. experimental results show reasonably efficiently deal with uncertainty assessment respect ranking reliability ranking.