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.

Due to the complexity of the real world, effective consideration of the ambiguity and reliability of information is a challenge that must be addressed by the correct decision of the expert system. Z-number provides us with a good idea because it describes the probability of the random variable and the possibility measure. Recently, Yager presented a soft likelihood function that effectively combines probabilistic evidence to deal with the conflict information. This article generalizes Yager's soft likelihood function based on Z-numbers and proposes a Z-numbers soft likelihood function (ZSLF) decision model. The application examples show the rationality and effectiveness of the method. The comparison and discussion further show the advantages of the ZSLF decision model.

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.