Marginalization in random permutation set theory: from the cooperative game perspective

Random permutation set theory (RPST), as an uncertainty modeling approach considering underlying ordered information, is proposed based on permutation set recently. Different from Dempster–Shafer Theory (DST), RPST extends the event space from power sets to permutation sets and thus can distinguish weights between ordered sets of the same cardinality. In this paper, we use an n -player cooperative game to interpret RPST and propose an OWA operator-based method to calculate the marginalizations of Permutation Mass Function (PerMF). In addition to reflecting the ordered information of the permutation events, the proposed method also relates the Probability Mass Function (ProbMF), the Basic Probability Assignment (BPA) and the PerMF from the perspective of random sets.