现实世界中存在着大量模糊性和不确定性的信息和数据，而Fuzzy集及其的推广Vague集等理论的提出为解决这些不确定问题提供了一种很好的方法和工具. 相似性度量作为Vague集理论的主要研究内容之一，受到了研究者的广泛关注. 目前许多研究者已经提出了大量的Vague集相似度量方法，但是这些方法能区分的Vague集是有限的. 因此，通过构造新的相似度量公式寻找Vague集相似度量方法，或者提出新的扩展集进行相似度量公式的构造是很有必要的. 本文主要内容如下.

首先，针对已有相似度量方法考虑因素不全面的情况，本文从二次投票出发同时考虑了二次投票中支持度、反对度和未知度的包含关系，合理设置系数，提出一种新的基于二次投票的Vague集相似度量方法，同时对新相似度量方法进行理论证明. 分别选取小样本和大样本与已有相似度量方法进行比较，提出了一种新的相似度区分能力的定义. 实验结果表明无论是小样本数据还是大样本数据，相比于已有的相似度量方法，本文提出的相似度量方法区分能力都是最高的.

其次，考虑到双极性理论和软集理论在处理不确定和不精确信息方面巨大优势，本文在Vague集理论中引入了双极性理论和软集理论，在此基础上提出了双极性Vague软集的概念. 给出了双极性Vague软集理论框架，包括相对补、狭义并、狭义交等定义；双极性Vague软集的相等、包含等代数关系；吸收律、交换律、结合律等基本运算以及双极性Vague软集相似度量的定义；并且对相关性质和双极性Vague软集相似度量的定义正确性进行了证明. 最后，以0. 1为步长进行遍历得到(4356*4356)组数据，计算新的双极性Vague软集相似度量区分能力为14. 4，与Vague集相比在样本扩大4356倍的情况下其区分能力依旧很高，充分的体现出了其有效性.

最后，在相同的数据下，将本文提出的Vague集相似度量方法和双极性Vague软集相似度量方法应用于聚类分析和多准则决策中. 通过比较分析发现，新提出的Vague集相似度量方法能够有效和合理的区分数据，而新提出的双极性Vague软集相似度量方法不仅增加了数据捕获能力，而且解决了Vague集相似度量的参数不兼容问题，从而为处理不确定信息和数据提供了更实用的方法.

Things in reality are not necessarily one or the other, so there is a lot of ambiguity and uncertainty of information and data. Fuzzy sets and their generalized Vague sets theory provide a good method and tool for solving many fuzzy problems in real world. Similarity measurement, as one of the main contents of Vague set theory, is widely concerned by vague set researchers. Although similarity measurement methods of Vague sets have been proposed by many vague sets, the vague sets can be distinguished by these methods are limited. Therefore, it is necessary to find similarity measure method of Vague set by constructing new similarity measure formula, or propose new extended set to construct similarity measure formula. The main contents of this paper are as follows.

First of all, in view of the incomplete consideration of factors in the existing similarity measurement method, this paper considers the inclusion relation of Vague set of similarity measurement, support degree, opposition degree and unknown degree from secondary voting, sets reasonable coefficients, proposes a new similarity measurement method based on vague set of secondary voting, and proves theoretically that the new similarity measurement method meets the basic criteria of similarity measurement. Small samples and large samples were selected respectively to compare with the existing similarity measurement methods, and a new definition of similarity differentiation ability was proposed. The experimental results show that the similarity measurement method proposed in this paper has the highest distinguishing ability compared with the existing similarity measurement methods, no matter small sample data or large sample data.

Secondly, considering the huge advantage of bipolar Vague and soft set theory in dealing with uncertain and inaccurate information, this paper introduces bipolar Vague theory and soft set theory in vague set theory, based on which the concept of bipolar Vague soft set is proposed. The theoretical framework of bipolar Vague soft sets is given, including the definitions of relative complement, narrow union and narrow intersection. Algebraic relation of equality and inclusion of bipolar Vague soft sets; The basic operations of absorption law, commutative law, associative law and the definition of similarity measure of bipolar Vague soft sets are discussed. The correctness of definition of similarity measure of relative properties and bipolar Vague soft sets is proved. Finally, a set of (4356*4356) data is obtained by walking 0.1 step. The similarity measure differentiation ability of the new bipolar Vague soft set is calculated to be 14.4, which is still very high even when the sample size is expanded 4356 times compared with Vague set, fully reflecting its effectiveness.

Finally, similarity measure of Vague sets and bipolar Vague soft sets proposed in this paper are applied to cluster analysis and multi-criteria decision making under the same data. By comparison and analysis, it is found that the new similarity measure method of Vague sets can distinguish data effectively and reasonably, while the new similarity measure method of Vague sets not only increases the ability of data acquisition, but also solves the incompatibility of parameters of Vague sets similarity measure, thus providing a more practical method for processing uncertain information and data.