Uncertainty management with quantitative propensity matrix in random permutation set theory

Abstract

The refined belief structure provides a more comprehensive capability for handling uncertain information. As an emerging belief model, the random permutation set (RPS) can be viewed as a layer-2 belief structure. Unlike fuzzy belief structures, RPS achieves precision without complex computations, as sequential calculations are more manageable. Previous studies typically assume a fixed and equidistant model for weak propensities in RPS. However, in practice, RPSs from different sources often fail to satisfy this assumption. This paper proposes the Quantitative Propensity Matrix (QPM) to distinguish the relative importance of elements within an ordered focal set and introduces a fusion method to integrate weak propensities across various RPSs. The QPM also enables the transformation of permutation mass functions (Perms) into probability mass functions (ProbMFs) through weight allocations. Given the varying reliability of information sources, the proposed method is applied to multi-source information fusion and decision-making processes. Some numerical experiments demonstrate the effectiveness of the proposed approach.