勾股模糊集的距离测度及其在多属性决策中的应用  

Distance measures of pythagorean fuzzy sets and their applications in multiattribute decision making

作　　者：李德清[1,2] 曾文艺[2] 尹乾[2] LI De-qing ZENG Wen-yi YIN Qian(Department of Basics, Ordnance Engineering College, Shijiazhuang 050003, China College of Information Science and Technology, Beijing Normal University, Beijing 100875, China)

机构地区：[1]军械工程学院基础部,石家庄050003 [2]北京师范大学信息科学与技术学院,北京100875

出　　处：《控制与决策》2017年第10期1817-1823,共7页Control and Decision

基　　金：国家自然科学基金项目(10971243;61472043)

摘　　要：首先,讨论3种勾股模糊数排序方法的特点,指出其中两种排序方法的不足;其次,研究勾股模糊集的结构特征,指出勾股模糊数本质上由隶属度、非隶属度、自信度和自信度方向4个特征参数完全刻画;再次,利用上述4个参数分别构造勾股模糊数和勾股模糊集之间的海明距离、欧几里得距离和闵可夫斯基距离,并研究这些距离公式的性质;最后,借助理想点法给出基于勾股模糊集距离的多属性决策方法,并通过实例验证所提方法的合理性.Firstly, via comparing the features of intuitionistic fuzzy set（FS） and Pythagorean fuzzy set（PFS）, three ranking methods for Pythagorean fuzzy numbers（PFNs） are analyzed, and some flaws of two ranking methods are pointed out.Then, it is illuminated that each PFN is characterized by four parameters, i.e., the membership degree, the nonmembership degree, the strength of commitment and the direction of strength. Simultaneously, the distance measures of PFSs and PFNs are investigated. The Hamming distance measure, the Euclidean distance measure and the Minkowski distance measure between PFSs and PFNs are proposed, and the desired properties are discussed. Finally, a multiple attribute decision making method in the Pythagorean fuzzy environment based on the proposed distance measures is presented. A numerical example is provided to illustrate the validity and applicability of the presented approach.

关 键 词：直觉模糊集 勾股模糊集 勾股模糊数 勾股模糊数排序 距离 

分 类 号：O159[理学—数学]