In Dempster–Shafer evidence theory, how to use the basic probability assignment (BPA) in decision-making is a significant issue. The transformation of BPA into a probability distribution function is one of the common and feasible schemes. To overcome the problems of the existing methods, we propose a marginal probability transformation method based on the Shapley value approach. The proposed method allocates BPA values in terms of how much an element contributes to a set, which is an equitable and effective distribution mechanism. Furthermore, we use probabilistic information content to evaluate the effect of each transformation method. Moreover, some numerical examples are used to demonstrate the efficiency and feasibility of the proposed method. Further, two applications, target recognition, fault diagnosis are used to verify the superiority and effectiveness of the proposed method in practice.

Information fusion is an important research direction. In this field, there are plenty of ways to combine evidence. Initially, Yager proposed a soft-likelihood function based on the ordered weighted average (OWA) operator to effectively fuse compatible probabilistic evidence. Recently, Song et al proposed a new soft-likelihood function based on the power ordered weighted average (POWA) operator. However, through analysis, we find Song et al's method has the following two shortcomings: (a) The weight of POWA cannot comprehensively reflect the relation between probability and OWA operator. (b) The soft-likelihood function does not reflect the preferences of decision makers. To overcome the above problem, we propose a modified soft-likelihood function. The effectiveness of the proposed method is demonstrated from the perspective of theoretical analysis and numerical examples.

The negation of probability distribution becomes an important topic since some problems are burdensome to deal with directly. Inspired by Yager's negation of probability distribution, an extension model to measure the negation of a probability distribution is proposed using the idea of a nonextensive statistic based on Tsallis entropy. Proofs show that the proposed extension of negation of probability distribution converges to the maximum Tsallis entropy. The proposed model may extend Yager's method to consider the influences of the correlations in a system, which gives the different convergent routes. Some numerical simulation results are used to illustrate the effectiveness of the proposed methodology.

In the application of Z-number, how to generate Z-number is a significant and open issue. In this paper, we proposed a method of generating Z-number based on the OWA weights using maximum entropy considering the attitude (preference) of the decision maker. Some numerical examples are used to illustrate the effectiveness of the proposed method. Results show that the attitude (preference) of the decision maker can give an optimal possibility distribution of the reliability for Z-number using maximum entropy.