In this paper, a multi-object recognition scenario is considered to extend the random finite set into random permutation set. Probabilistic information on random permutation set can be viewed as an distribution determined by three random variables. We use another emerging uncertainty representation, order-2 information granule, to realize the probabilistic information fusion on random permutation sets. First, the probabilistic information on random permutation sets is viewed as an order-2 probability distribution. Second, corresponding information fusion approach is proposed. Finally, the proposed approach is applied to random permutation sets, resolving the decision-making issue under the multi-object recognition scenario. This paper pioneers the connection of order-2 information processing logic to a multi-object recognition task and develops order-2 probability distribution and its combination rules. Compared to the traditional probabilistic information fusion approaches, the proposed approach takes into account not only the propositions’ beliefs provided by the sources, but the structural dependency among propositions as well.

The research on uncertainty is a hot spot in artificial intelligence, especially in actual applications. Most research focus on measuring the uncertainty between evidence, ignoring the structure of evidence. When a sample has multiple features, the traditional structure of the focal element cannot handle and display the uncertainty between multiple features directly. Hence, we proposed a new structure of the focal element considering multiple features into one focal element and provided the corresponding basic probability assignment calculation. To apply the new structure in practices, we provided a new object recognition method combining the fractal feature and credible evidence. The new method can improve the robustness of the algorithm in a noisy environment. In the end, some experiments have illustrated the validity and correctness of the proposed method.

Dempster–Shafer evidence theory (evidence theory) has been widely used as an efficient method for dealing with uncertainty. In evidence theory, Dempster's rule is the most well-known evidence combination method but it does not work well when the evidence is in high conflict. To improve the performance of combining conflicting evidence, an original and novel evidence combination method is presented based on the Pearson correlation coefficient and weighted graph. The proposed method can correctly recognize the alternative situation with a high accuracy. Besides, the convergence performance of this method is better when compared with other combination rules. In addition, the weighted graph generated by the proposed method can directly represent the relationship between different evidence, which can help researchers estimate the reliability of different body of evidence. Our experimental results indicate the advantages of our proposed evidence combination rule over existing methods, and the results are analyzed and discussed.

Information quality has received extensive attention recently. Yager and Petry proposed an information quality suitable for the framework of probability theory, and proposed a method of fusing multisource information, which can improve the information quality required for decision-making. Then, Bouhamed et al. extended information quality to the theory of possibility. However, the basic probability assignment (BPA) in evidence theory can deal with uncertainty more effectively. Therefore, this work provides a companion paper that makes the method applicable to evidence theory. This method uses vector notation to represent B P A. A fusion method is designed to select the best quality subset based on two factors: information quality and source credibility function, and using the score function to verify the quality of each subset. Finally, a numerical example details the eight steps of the method, and uses the Iris data set and banknote authentication data set to illustrate the application of the method in pattern recognition.

Dempster-Shafer (D-S) evidence theory has been used in many fields due to the flexibility and effectiveness in modelling uncertainties, which is the extension of classical probability. Uncertainty principle is one of the most important principles in quantum theory, which has been used in many fields. How to set the connection between quantum theory and D-S evidence theory is also an open issue. Hence, the paper proposed the quantum model of mass function to consider the quantum theory and D-S evidence theory. In the proposed quantum method, quantum mass function uses euler formula to represent. The paper also discusses some operations based on the quantum model of the mass function. Moreover, the paper also discusses the relationship between quantum mass function and classical mass function by using some numerical examples. Classical mass function is a special case when there is no interference in quantum mass function. Similar to the other quantum models, this study provides a more wide application in quantum information.

Because of the superiority in dealing with uncertainty expression, Dempster-Shafer theory (D-S theory) is widely used in decision theory. In D-S theory, the basic probability assignment (BPA) is the basis and core. Recently, some researchers represent BPA on a N-dimension frame of discernment (FOD) as 2 N -dimension vector in Descartes coordinate system. This representation treats a BPA as a point in the 2 N -dimensional space. A new vector and geometry interpretation of BPA is proposed in this paper. The BPA on a N-dimension FOD is represented as N-dimension vector with parameters in this method. Then BPA is expressed as subset of N-dimension Cartesian space rather than a point. The proposed method is a new way to represent BPA with vector and geometry. The essence of this method is to convert BPA to probability distribution with parameters. The applications of this representation method in D-S theory have been studied. Based on this method, problems in D-S theory can be solved, which include the fusion of BPAs, the distance between BPAs, the correspondence between BPA and probability, and the entropy of BPAs.

The conflict problem in D-S evidence theory has attracted the attention of many scholars. Conflict coefficients are proposed to describe conflicts between bodies of evidence. The association coefficient as the opposite of the conflict coefficient is also used to measure the conflict. The larger the association coefficient, the smaller the conflict degree, and the higher the similarity between the evidence bodies, and vice versa. In this paper, the degree of association is defined by Deng Entropy, and a new association coefficient is proposed based on the basic inequality. The nature of the new association coefficient and conflict coefficients is explored using examples. Finally, the association coefficient combined with the D-S combination rule is applied to the target recognition system, and accurate results are obtained.

Entailment for measure-based belief structures can extend the possible probability value range of variables on a space and obtain more information from variables. However, if the variable space comes from intuitionistic fuzzy sets, the classical entailment for measure-based belief structures will not work in this issue. To deal with this situation, we propose the entailment for intuitionistic fuzzy sets based on generalized belief structures in this paper to apply the entailment for measure based belief structures on space, which is made up of non-membership degree, membership degree and hesitancy degree of a given intuitionistic fuzzy sets. Numerical examples are mentioned to prove the effectively and flexibility of this proposed entailment model. The experimental results indicate that the proposed algorithm can extend the possible probability value range of variables of space efficiently and obtain more information from intuitionistic fuzzy sets.

Information fusion under extremely uncertain environments is an important issue in pattern classification and decision-making problems. The Dempster-Shafer evidence theory (D-S theory) is more and more extensively applied in dealing with uncertain information. However, the results contrary to common sense are often obtained when combining different evidence using Dempster's combination rule. How to measure the difference between different evidence is still an open issue. In this paper, a new divergence is proposed based on the Kullback-Leibler divergence to measure the difference between different basic probability assignments (BPAs). Numerical examples are used to illustrate the computational process of the proposed divergence. Then, the similarity for different BPAs is also defined based on the proposed divergence. The basic knowledge about pattern recognition is introduced, and a new classification algorithm is presented using the proposed divergence and similarity under extremely uncertain environments. The effectiveness of the classification algorithm is illustrated by a small example handling robot sensing. The proposed method is motivated by the urgent need to develop intelligent systems, such as sensor-based data fusion manipulators, which are required to work in complicated, extremely uncertain environments. Sensory data satisfy the conditions (1) fragmentary and (2) collected from multiple levels of resolution.

Dempster-Shafer evidence theory has been widely used in many applications due to its advantages with weaker conditions than Bayes probability. How to measure the uncertainty of basic probability assignment (BPA) in Dempster-Shafer evidence theory is an open and essential issue. Tsallis entropy as nonextensive entropy proposed according to multifractals has been used in many fields. In this paper, a new uncertainty measure of BPA is presented based on Tsallis entropy. The key issue is to determine the value of q in Tsallis entropy. In addition, this paper also analyzes the properties of proposed uncertainty measure. Some numerical examples are used to illustrate the efficiency of the proposed method. Finally, the paper also discusses the application of the proposed method in decision-making.

Maxitive Belief Structures (MBSs), emerge as a novel class of belief structure to represent imprecise and uncertain information with a specific structure allowing it to model both probability nonspecificity and imprecise. A novel matrix game with payoffs of MBS is presented. The proposed model can be used to describe interactions among players, and an effective method is developed to find the solution of a game through reaching an equilibrium point. A numerical example is given to verify the validness of the proposed model.

How to efficiently handle uncertain information is still an open issue. In this paper, a new method to deal with uncertain information, named as two-dimensional belief function (TDBF), is presented. A TDBF has two components, T = (), both and are classical belief functions, while is a measure of reliable of . The definition of TDBF and the discounting algorithm are proposed. Compared with the classical discounting model, the proposed TDBF is more flexible and reasonable. Numerical examples are used to show the efficiency and application of the proposed method.

Dempster-Shafer is widely used to address the problems of uncertainty. One assumption mentioned in this theory is that the distribution of information should be independent. In practice, the requirement cannot be fulfilled. One of the efficient methods to deal with dependent evidence is to calculate the correlation discounting. However, existing coefficient can only be applied to show the direct relation between evidence A and B but do not take the indirect relationship into consideration. To address this issue, in this paper, a new method to combine dependent evidence based on decision-making trial and evaluation laboratory is presented, not only considering the relation between evidence A and B and the relation between evidence B and C, but also considering the transitive influence between evidence A and C. Finally, the experiments on some benchmark data sets are illustrated to show the efficiency of the proposed method.

D numbers has been previously introduced in linguistic decision making due to its effectiveness and flexibility in dealing with uncertain information. The study applies the integration operator of D numbers to obtain the decision result by aggregating different opinions of experts which may be imprecise and uncertain. However, sometimes it would be more reasonable to consider the risk preference of the decision maker. In this paper, we proposed an improved aggregating method for linguistic information based on D numbers and OWAWA operator. The main advantage is that it can integrate the degree of importance that each experts has and the risk preference of the decision maker in the aggregation of linguistic information. An example is used to demonstrate the flexibility and reasonability of the proposed method.

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.

Many relations in the real world can be described by mathematical language. Fuzzy set theory can transform human language into mathematical language and use membership degree function to describe relations between events. Dempster–Shafer evidence theory provides basic probability assignment (BPA), which can describe the occurrence rate of attributes in basic events. Based on the known membership degree function and BPA distribution, a new evaluation method is proposed in this paper to analyze decision making. Given the relations among relevant events, which are expressed by BPA distribution and membership degree function, the relations among basic events and top event can be obtained. The Dempster's combination rule and pignistic probability transformation are used to transform BPA distribution into probability distribution. The belief measure is applied to deal with these fuzzy relations. Some numerical examples are given in this paper to illustrate the proposed evaluation methodology.

One of the key issues in the application of the Dempster–Shafer evidence theory is the transformation between basic probability assignments (BPAs) and probability. In this paper, new probability transformation based on the ordered visibility graph (OVG) is proposed to solve the decision-making problem. In the proposed transformation, an OVG can be constructed based on the BPAs. From this OVG, the network of focal elements can be obtained. The degree of a node in the network represents its weight, which is essential to the transformation. Based on these weights, the probability results are obtained. Some illustrative cases are provided to demonstrate the effectiveness of the proposed probability transformation.

Dempster's rule of combination can only be used when the bodies of evidence are assumed to be independent. However, such an assumption is often unrealistic. This paper proposes a systematic approach to handle dependence in evidence theory. It includes both the representation of dependence among information sources and the aggregation of the dependent evidence. For the representation of the dependence, the proposed methodology is able to capture both inner dependence (i.e., dependence among features of a system) and outer dependence (i.e., dependence among the evidence sources during the information propagating and evaluating process). We suggest dealing with the inner dependence by applying the analytic network process model, and modeling the outer dependence based on the intersection situations of the identified influencing factors. Then for the combination of dependent evidence, the strategy is to use discounting aggregation where the discounting coefficients are related to the degree of both outer and inner dependence. The discounting operator helps reduce the duplicate calculations in the fusion of dependent evidence and relax the assumption of independence when using Dempster's rule. A case study of transportation project evaluation is used to illustrate the proposed methodology.