A FRACTAL-BASED PERMUTATION BELIEF ENTROPY FOR UNCERTAINTY MEASURE IN RANDOM PERMUTATION SET

Random permutation set (RPS), as a generalization of the traditional Dempster–Shafer evidence theory, has received a great deal of attention due to its ability to serve as an efficient representation of ordered uncertain information. Nonetheless, quantifying uncertainty within RPS remains a subject of ongoing research. In order to enhance decision-making capabilities, this paper proposes an RPS Pignistic probability transformation (RPPT) method, the core of which lies in fractal-inspired redistribution of the permutation mass function in the time dimension. Subsequently, based on RPS fractal process of Pignistic probability transformation, a new Fractal-based permutation belief (FPB) entropy is proposed to measure the uncertainty of RPS. The properties of FPB entropy are examined, and its reasonableness and efficacy are demonstrated through comparative analyses with existing entropies. Finally, experimental comparisons proved the effectiveness of the proposed entropy in practical applications.