Abstract
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.
Highlights
IntroductionWith the sharply growing interest in data fusion, the evidence theory, known as the Dempster–Shafer (D–S) theory [1], which was first presented by Dempster [2] and developed by Shafer [3], has aroused great concern for its effectiveness in modeling and fusing uncertain information [4]
With the sharply growing interest in data fusion, the evidence theory, known as the Dempster–Shafer (D–S) theory [1], which was first presented by Dempster [2] and developed by Shafer [3], has aroused great concern for its effectiveness in modeling and fusing uncertain information [4].D–S theory assigns probabilities to the power set of events [5], so it has advantages of dealing with uncertainty and unknown problems
Shannon entropy has basically resolved the uncertainty of probability theory [26], which is widely used in many application systems [27,28,29]
Summary
With the sharply growing interest in data fusion, the evidence theory, known as the Dempster–Shafer (D–S) theory [1], which was first presented by Dempster [2] and developed by Shafer [3], has aroused great concern for its effectiveness in modeling and fusing uncertain information [4]. In D–S theory, there is an open issue on how to measure the uncertainty of belief functions [2,5,21,22]. The basic probability assignment (BPA) function is transformed into probability distribution through conversion, which results in the loss of information. Deng et al [42] have improved this measure to avoid counter-intuitive results caused by it They overcome some shortcomings of traditional measurement; the uncertainty of those methods is inconsistent with Shannon entropy when BPA is degenerated to probability distribution. We analyze the uncertainty of BPA based on intervals which contain more information than probability. We propose new belief entropy by combining probability interval and.
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