Probability transformation of mass function: A weighted network method based on the ordered visibility graph

Transform of basic probability assignment to probability distribution is an important aspect of decision making process. To address this issue, a weighted network method based on the ordered visibility graph is proposed in this paper, named OVGWP. In this proposed method, the information volume of focal elements is calculated by belief entropy. The entropy value is used to determine the rank of each proposition. After generating the rank, a weighted network corresponding to the given basic probability assignment can be constructed. The global ratio for proportional belief transformation is determined by the degree of nodes and its weighted edges in the network. Compared with existing ordered visibility graph probability, we have considered not only the belief value itself, but also the cardinality of basic probability assignment. Hence the proposed OVGWP considers a much more comprehensive information for transformation. Experimental results reveal that OVGWP produces an effective and reasonable transformation performance compared with existing methods. If the basic probability assignment is given as m ( Θ ) = 1, the proposed OVGWP has the same result with pignistic probability transformation. The proposed OVGWP satisfies the consistency of the upper and lower boundaries.

Authors

• Luyuan Chen Beijing Information Science and Technology University
• Yong Deng State Grid Fujian Electric Power Co.
• Kang Hao Cheong

Keywords

• Dempster–Shafer evidence theory
• Probability transformation
• Visibility graph
• Belief entropy