A Novel Belief Entropy for Measuring Uncertainty in Dempster-Shafer Evidence Theory Framework Based on Plausibility Transformation and Weighted Hartley Entropy

Abstract

Dempster-Shafer evidence theory (DST) has shown its great advantages to tackle uncertainty in a wide variety of applications. However, how to quantify the information-based uncertainty of basic probability assignment (BPA) with belief entropy in DST framework is still an open issue. The main work of this study is to define a new belief entropy for measuring uncertainty of BPA. The proposed belief entropy has two components. The first component is based on the summation of the probability mass function (PMF) of single events contained in each BPA, which are obtained using plausibility transformation. The second component is the same as the weighted Hartley entropy. The two components could effectively measure the discord uncertainty and non-specificity uncertainty found in DST framework, respectively. The proposed belief entropy is proved to satisfy the majority of the desired properties for an uncertainty measure in DST framework. In addition, when BPA is probability distribution, the proposed method could degrade to Shannon entropy. The feasibility and superiority of the new belief entropy is verified according to the results of numerical experiments.

An Improved Belief Entropy to Measure Uncertainty of Basic Probability Assignments Based on Deng Entropy and Belief Interval

“…Here, the belief interval , which contains more information of D-S framework is often overlooked. There are only several articles about uncertainty measurement mentioning the belief interval [ 5 , 46 , 47 , 49 , 50 , 52 ]. In this article, an improved belief entropy involving the belief interval is proposed based on Deng entropy and the belief interval, defined as follows: …”

“…The number of elements in the proposition A changes from 1 to 14. To verify the advantages of the improved belief entropy, another eight uncertainty measures are introduced for comparison: Deng entropy [ 43 ], Höhle’s confusion measure [ 38 ], Yager’s dissonance measure [ 39 ], Dubois and Prade’s weighted Hartley entropy [ 37 ], Klir and Ramer’s discord measure [ 35 ], Klir and Parviz’s strife measure [ 40 ], George and Pal’s conflict measure [ 51 ], Pan and Zhou’s measure [ 50 ] and Zhou et al’s measure [ 4 ].…”

“… Comparison among different uncertainty measures (Pan and Zhou [ 50 ], Yager [ 39 ], Deng Entropy [ 43 ], Dubois and Prade [ 37 ], Höhle [ 38 ], Klir and Ramer [ 35 ], Klir and Parviz [ 40 ], George and Pal [ 51 ], Zhou et al [ 4 ], and Improved entropy). …”

Research on the Combination Method of Temporal Conflict Evidence Based on Transition Matrix

“…With the information entropy approach, the uncertainty of the evidence is characterized by entropy [13][14][15][16], which is based on the information carried by the evidence itself. Deng [17] proposed a new measure based on the entropy of basic probability distribution uncertainty, which is an extension of Shannon entropy.…”

Entropy Measures for Data Analysis: Theory, Algorithms and Applications

“…Some distance and entropy measures for CCVSs are axiomatically defined and relations between them are investigated. The work [ 12 ] of Pan et al focuses on Dempster–Shafer evidence theory, which can be considered as a generalization of probability theory. A new belief entropy, measuring uncertainty in this framework, and its performance are discussed on the base of numerical experiments.…”