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首页> 外文期刊>Applied Intelligence: The International Journal of Artificial Intelligence, Neural Networks, and Complex Problem-Solving Technologies >Uncertainty measure in evidence theory with its applications
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Uncertainty measure in evidence theory with its applications

机译：证据理论的不确定性措施及其应用

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摘要

Uncertainty measure in evidence theory supplies a new criterion to assess the quality and quantity of knowledge conveyed by belief structures. As generalizations of uncertainty measure in the probabilistic framework, several uncertainty measures for belief structures have been developed. Among them, aggregate uncertainty AU and the ambiguity measure AM are well known. However, the inconsistency between evidential and probabilistic frameworks causes limitations to existing measures. They are quite insensitive to the change of belief functions. In this paper, we consider the definition of a novel uncertainty measure for belief structures based on belief intervals. Based on the relation between evidence theory and probability theory, belief structures are transformed to belief intervals on singleton subsets, with the belief function Bel and the plausibility function Pl as its lower and upper bounds, respectively. An uncertainty measure SU for belief structures is then defined based on interval probabilities in the framework of evidence theory, without changing the theoretical frameworks. The center and the span of the interval is used to define the total uncertainty degree of the belief structure. It is proved that SU is identical to Shannon entropy and AM for Bayesian belief structures. Moreover, the proposed uncertainty measure has a wider range determined by the cardinality of discernment frame, which is more practical. Numerical examples, applications and related analyses are provided to verify the rationality of our new measure.
机译：证据理论的不确定性措施提供了一种评估信仰结构所传达的知识的质量和数量的新标准。作为概率框架的不确定性措施的概括，已经开发了一些信念结构的不确定性措施。其中，总不确定性AU和歧义度量是众所周知的。然而，证据和概率框架之间的不一致导致现有措施的限制。它们对信仰功能的变化非常不敏感。在本文中，我们考虑了基于信念间隔的信仰结构的新颖性不确定性措施的定义。基于证据理论与概率理论之间的关系，信仰结构转变为单例子集的信仰间隔，分别具有信仰功能BEL和合理功能PL分别为下限和上限。然后基于证据理论框架中的间隔概率来定义信仰结构的不确定性测量SU，而不改变理论框架。该中心和间隔的跨度用于定义信念结构的总不确定性程度。事实证明，苏与香农熵和贝叶斯信仰结构相同。此外，所提出的不确定度量具有由识别框架的基数确定的更广泛的范围，这更加实用。提供了数值例子，应用和相关分析来验证我们新措施的合理性。

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