Abstract

In this study, we consider a new aspect of belief function or Dempster-Shafer theory to define a belief set and cosine similarity measure between two belief sets under uncertainty. For this purpose, firstly, the concept of belief sets will be represented as a triple vector space that is characterized by truth-belief degree, uncertainty-belief degree; and falsity-belief degree. Then, the cosine similarity measure between two belief sets is proposed to determine the degree of similarity between them. This measure is directly defined upon the framework of Dempster-Shafer theory without switching by other theories. Finally, an application of a new method in the decision-making process is provided in the medical diagnosis, when values were presented on the structure of belief set. Furthermore, a numerical example of the medical diagnosis is presented to show the effectiveness and flexibility of the proposed method.

摘要

在这项研究中，我们考虑了信念函数或 Dempster-Shafer 理论的一个新方面来定义不确定性下两个信念集之间的信念集和余弦相似性度量。为此，首先，信念集的概念将被表示为一个三元向量空间，其特征为真值信度、不确定度信度；和误信度。然后，提出了两个信念集之间的余弦相似度度量来确定它们之间的相似度。该度量直接定义在 Dempster-Shafer 理论的框架上，无需转换其他理论。最后，在医学诊断中提供了一种新方法在决策过程中的应用，即在信念集结构上呈现值。此外，