Cosine Distance Measure between Neutrosophic Hesitant Fuzzy Linguistic Sets and Its Application in Multiple Criteria Decision Making
Cosine Distance Measure between Neutrosophic Hesitant Fuzzy Linguistic Sets and Its Application in Multiple Criteria Decision Making
复制标题
中智犹豫模糊语言集之间的余弦距离测度及其在多准则决策中的应用
DOI：
10.3390/sym10110602
复制
发表时间：
2018-11-01
期刊：
影响因子：
2.7
通讯作者：
Peng, Dan
中科院分区：
文献类型：
--
作者：
Liu, Donghai;Chen, Xiaohong;Peng, Dan
本文在犹豫模糊语言术语集（HFLTS）和中智集合（NS）的基础上提出了中智犹豫模糊语言术语集（NHFLTS），能够灵活表达多准则决策问题中的不一致和不确定性信息。还讨论了基于语言尺度函数的NHFLTS的基本运行规律。然后我们提出了广义中智犹豫模糊语言距离测度并讨论了它的性质。此外，NHFLTS新的相似性测度结合了广义中智犹豫模糊语言距离测度，并给出了余弦函数。根据相似性度量和距离度量之间的关系，提出了NHFLTS之间相应的余弦距离度量，并且我们开发了通过与理想解相似度（TOPSIS）方法对所获得的余弦距离度量进行顺序偏好的技术。所提出的 NHFLTS 的主要优点是在语言尺度函数上定义，决策者可以灵活地将语言信息转换为语义值，并且所提出的 NHFLTS 之间的余弦距离度量与 TOPSIS 方法不仅可以从代数的角度，而且可以从几何的角度处理相关的决策信息。最后，通过示例证明了该方法的合理性和有效性，并与其他现有方法进行了比较。
This paper proposes a neutrosophic hesitant fuzzy linguistic term set (NHFLTS) based on hesitant fuzzy linguistic term set (HFLTS) and neutrosophic set (NS), which can express the inconsistent and uncertainty information flexibly in multiple criteria decision making problems. The basic operational laws of NHFLTS based on linguistic scale function are also discussed. Then we propose the generalized neutrosophic hesitant fuzzy linguistic distance measure and discuss its properties. Furthermore, a new similarity measure of NHFLTS combines the generalized neutrosophic hesitant fuzzy linguistic distance measure and the cosine function is given. A corresponding cosine distance measure between NHFLTSs is proposed according to the relationship between the similarity measure and the distance measure, and we develop the technique for order preference by similarity to an ideal solution (TOPSIS) method to the obtained cosine distance measure. The main advantages of the proposed NHFLTS is defined on linguistic scale function, the decision makers can flexibly convert the linguistic information to semantic values, and the proposed cosine distance measure between NHFLTSs with TOPSIS method can deal with the related decision information not only from the point of view of algebra, but also from the point of view of geometry. Finally, the reasonableness and effectiveness of the proposed method is demonstrated by the illustrative example, which is also compared to the other existing methods.