Dempster-Shafer evidence theory has wide applications in many fields. Recently, A new entropy called Deng entropy was proposed in evidence theory. Some scholars have pointed out that Deng Entropy does not satisfy the additivity in uncertain measurements. However, irreducibility may have a huge effect. The derived entropy from complex systems is often irreducible. Inspired by this, generalized belief entropy is proposed. The belief entropy implies the relationship between Deng entropy, Rényi entropy, Tsallis entropy. In addition, numerical examples demonstrate the flexibility of the proposed Rényi-Deng (R-D) entropy to measure the uncertainty of basic probability assignment (BPA). Finally, a method for identifying contradictory evidence based on Rényi-Deng (R-D) entropy is proposed. The experiment show the effectiveness of the proposed method.
In many cases, we obtain information using various methods in order to make better decisions. The everything in nature and society has its negative, the negation of negation has significant meaning. Considering the problem from two aspects, we can get more accurate information. However, in most cases, the information of negation is ignored. Hence, the negation provides a new view to obtain information. However, existing negation method mainly apply to probability distribution. How to get the negation of basic probability assignment (BPA) in Dempster-Shafer (D-S) theory is still an open issue. The paper proposed the new negation method of BPA. Besides, some numerical examples are given to this approach for better understanding. Moreover, in order to demonstrate the efficiency of the proposed method, the paper compared the changes of uncertainty between original and negation by using some uncertain measurement methods. Finally, practical application is used to be discussed the application of proposed method.
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]
Target recognition in uncertain environments is a hot issue. Fusion rules are used to combine the sensor reports from different sources. In this situation, obtaining more information to make correct decision is an essential issue. Probability distribution is one of the most used methods to represent uncertainty information. In addition, the negation of probability distribution provides a new view to represent the uncertainty information. In this article, the existing negation of probability distribution is extended with Tsallis entropy. The main reason is that different systems have different parameter q. Some numerical examples are used to demonstrate the efficiency of the proposed method. Besides, the article also discusses the application of negation in target recognition based on sensor fusion to further demonstrate the importance of negation.
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. K E Y W O R D S basic probability assignment, belief function, Dempster-Shafer evidence theory, mass function, quantum theory
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