论文标题
D数理论中的基本概念，定义和方法
Basic concepts, definitions, and methods in D number theory
论文作者
论文摘要
作为对Dempster-Shafer理论的概括，D数字理论（DNT）旨在提供一个框架，以不明确性和不完整来处理不确定的信息。尽管在先前的研究中，DNT有一些进步，但是它们缺乏系统性，并且尚未解决许多重要的问题。在本文中，考虑了构建DNT完美而系统的框架的几个关键方面。首先，正式定义和讨论了DNT中的非排斥性。其次，通过扩展以前的独家冲突重新分配（ECR）规则，提出了一种结合多个D数字的方法。第三，定义了一对新的信念和合理性指标，并通过提出的措施满足了许多理想的特性。第四，专门研究了信息符号D数字的组合，以展示如何处理DNT中信息的不完整。在本文中，我们将在未来的研究中考虑相对数学定义，属性和定理，具体示例和应用。
As a generalization of Dempster-Shafer theory, D number theory (DNT) aims to provide a framework to deal with uncertain information with non-exclusiveness and incompleteness. Although there are some advances on DNT in previous studies, however, they lack of systematicness, and many important issues have not yet been solved. In this paper, several crucial aspects in constructing a perfect and systematic framework of DNT are considered. At first the non-exclusiveness in DNT is formally defined and discussed. Secondly, a method to combine multiple D numbers is proposed by extending previous exclusive conflict redistribution (ECR) rule. Thirdly, a new pair of belief and plausibility measures for D numbers are defined and many desirable properties are satisfied by the proposed measures. Fourthly, the combination of information-incomplete D numbers is studied specially to show how to deal with the incompleteness of information in DNT. In this paper, we mainly give relative math definitions, properties, and theorems, concrete examples and applications will be considered in the future study.
