A new belief structure based on cardinality measure

Belief structure is a very effective tool to represent unknown information, and it is widely used in information fusion. Measure is also a perfect tool for evaluating unknown information, and cardinality-based measure is one of the most popular measure theory. Recently, Yager proposed the conjunction of possibility measures, which can fuse possibility measures very efficiently and has promising aspects. However, how to efficiently integrate the cardinality-based measures is still an open issue. This paper proposes a new conjunction model to fuse two cardinality measures. Interestingly, the result of the fusion is still a measure and a cardinality measure. With the help of Choquet integral, a new belief structure based on cardinality measure is proposed, which is based on the proposed conjunction of cardinality measures. For each subset in the space, the new belief structure based on cardinality measure finds the related focal elements, and calculates the cert function values and poss function values of these focal elements. Based on these cert function values and poss function values, the belief and plausibility of the corresponding subset can be calculated, and the conjunction of cardinality measures plays a role in dividing the weight of focal elements in this process. This paper also proposes a simple calculation model for this new belief structure based on cardinality measure, which greatly reduces the computational complexity of the proposed model. Many theorems and proofs of the proposed models have been proposed. Numerical examples and practical application have been mentioned to reveal the high efficiency of the conjunction of cardinality measures and the new belief structure based on cardinality measure. The experimental results show that the proposed models can conjunct cardinality-based measures to a new cardinality measure successfully and solve the issues of decision making effectively.

Automated summary

The paper proposes a new conjunction model to fuse two cardinality measures and introduces a new belief structure based on cardinality measure. By calculating the cert and poss function values of focal elements, the belief and plausibility of the corresponding subset can be determined, with the conjunction of cardinality measures playing a crucial role in this process.