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]