Uncertainty measure based on Tsallis entropy in evidence theory

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.     

Evaluation method based on fuzzy relations between Dempster–Shafer belief structure

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.     

A new divergence measure for basic probability assignment and its applications in extremely uncertain environments

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.