Abstract

This study considers a new aspect of the belief function theory to define a belief set, which is characterized by truth, uncertainty and falsity belief degrees as a 3D vector representation. Then, based on the implication of a belief set, one of the similarity measures (i.e. Cosine, Jaccard and Dice) between two belief sets is defined. Furthermore, the weighted similarity measure of these different species between each alternative and ideal alternative is presented to rank alternatives and determine the best one. Finally, a comparison between similarity measures and an application of a new method based on similarity measures between two belief sets in the decision-making process is calculated to show the capability and validity of the proposed method.

摘要

本研究考虑了信念函数理论的一个新方面来定义一个信念集，其特征是真实、不确定和虚假信念度作为 3D 向量表示。然后，基于信念集的含义，定义两个信念集之间的相似性度量之一（即余弦、杰卡德和骰子）。此外，还提供了这些不同物种在每个备选方案和理想备选方案之间的加权相似性度量，以对备选方案进行排名并确定最佳方案。最后，计算了相似性度量之间的比较以及基于两个信念集之间的相似性度量的新方法在决策过程中的应用，以显示所提出方法的能力和有效性。