基于参考集的广义模糊数排序方法及在三支冲突分析中的应用  

Generalized fuzzy numbers ranking method based on reference set and its application in three-way conflict analysis

作　　者：周小锋 李小南 ZHOU Xiaofeng;LI Xiaonan(School of Mathematics and Statistics,Xidian University,Xi’an 710071,China)

机构地区：[1]西安电子科技大学数学与统计学院,陕西西安710071

出　　处：《西北大学学报(自然科学版)》2025年第2期355-365,共11页Journal of Northwest University(Natural Science Edition)

基　　金：国家自然科学基金(61976244)。

摘　　要：针对模糊数排序现有方法中参考集的选取带有盲目主观性的问题,提出了一种新的基于参考集和评价函数的广义模糊数排序方法。首先,该方法借助模糊距离定义参考集,其优点是能够减少因参考集预先给定或选取而增加的不确定性。其次,利用区间相似度和广义模糊数的质心构建评价函数,并给出了新的广义模糊数排序方法的框架。此外,通过实例将此方法与现有排序方法进行比较,验证了该方法的有效性和合理性。最后,将该方法应用于三支冲突分析中,评价不同方法所建立的联盟。In view of the blind subjectivity of reference set selection in the existing methods,this paper proposes a new generalized fuzzy number ranking method based on reference set and evaluation function.Firstly,the proposed method defines the reference set with the help of fuzzy distance,which has the advantage of reducing the uncertainty increased by the pre-given and selected reference set.Secondly,the evaluation function is constructed by using the centroid of interval similarity and generalized fuzzy numbers,and the framework of a new generalized fuzzy number ranking method is given.In addition,the effectiveness and rationality of the proposed method are verified by comparing it with the existing ranking methods by an example.Finally,the method is applied to the three-way conflict analysis to evaluate the alliances established by different methods.

关 键 词：广义模糊数 参考集 评价函数 模糊数排序 三支冲突分析 

分 类 号：O159[理学—数学]