How to measure the uncertainty of the basic probability assignment (BPA) function is an open issue in Dempster–Shafer (D–S) theory. The main work of this paper is to propose a new belief entropy, which is mainly used to measure the uncertainty of BPA. The proposed belief entropy is based on Deng entropy and probability interval consisting of lower and upper probabilities. In addition, under certain conditions, it can be transformed into Shannon entropy. Numerical examples are used to illustrate the efficiency of the new belief entropy in measurement uncertainty.

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.association coefficient, conflict coefficients, conflict problem, Deng entropy, D-S evidence theory, target recognition system | INTRODUCTIONThe D-S evidence theory was first proposed by Dempster 1 in 1967 and later developed by his student Shafer 2 in 1976 as an imprecise reasoning theory, which is widely promoted. [3][4][5][6] The theory was first applied to expert systems, 7-9 and it was gradually applied in the fields of information fusion, 10-12 intelligence analysis, 9,13-16 evidential reasoning, [17][18][19] and multiattribute decision analysis. [20][21][22][23][24] As an indeterminate reasoning method which satisfies the conditions weaker than Bayesian probability theory; it has the ability to directly express "uncertainty" 25 and "don't know." 26 Therefore, the D-S evidence theory is flexible and convenient for describing uncertainties. However, D-S evidence theory has produced counterintuitive results in the fusion of a highly conflicting example proposed by Zadeh. 27 Therefore, the issue of conflict between bodies of evidence has attracted more and more researchers so far. [28][29][30][31][32] Domestic and foreign scholars have proposed a large number of improved methods, which can be divided into two major categories: (a) modification of the combination rules of the classical D-S evidence theory to achieve the redistribution of conflicts in the case of evidence conflicts. [33][34][35][36] Such measures alleviate the conflict between the bodies of evidence to a certain extent, but at the same time, it is difficult for the new rules to maintain the original properties of the D-S combination rules. (b) Keep the classic combination rules unchanged, and preprocess conflict data before combination. [37][38][39][40][41][42] Haenni 43 believes that the modification of the data model is in engineering, mathematics and philosophically more reasonable. However, regardless of the type of method used to deal with conflicts between evidence, the conflict coefficient is an extremely important parameter. Therefore, the most critical step before choosing the right combination of evidence is the measure of evidence conflict.To measure the conflict between evidence bodies, many researchers have proposed...

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. K E Y W O R D S basic probability assignment, belief function, Dempster-Shafer evidence theory, Tsallis entropy, uncertainty | INTRODUCTIONUncertainty plays an important role in real-world and is inevitable in decision-making. 1-5 To handle uncertainty, a lot of theories have been developed, for example, probability theory, 6,7 Dempster-Shafer (D-S) evidence theory, 8,9 fuzzy sets, 10-13 gray model, 14 and Z number. [15][16][17][18] Among these methods, D-S evidence theory has attracted many research' attention due to its extension of Bayesian theory, [19][20][21][22] with the efficiency to deal with imprecise information. 8,23 Measuring the uncertainty of basic probability assignment function (BPA) in D-S theory is essential [24][25][26][27] and can be applied in many applications. [28][29][30]

Dempster-Shafer evidence theory can handle imprecise and unknown information, which has attracted many people. In most cases, the mass function can be translated into the probability, which is useful to expand the applications of the D-S evidence theory. However, how to reasonably transfer the mass function to the probability distribution is still an open issue. Hence, the paper proposed a new probability transform method based on the ordered weighted averaging and entropy difference. The new method calculates weights by ordered weighted averaging, and adds entropy difference as one of the measurement indicators. Then achieved the transformation of the minimum entropy difference by adjusting the parameter r of the weight function. Finally, some numerical examples are given to prove that new method is more reasonable and effective.

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