模糊关系的聚合及应用  

Aggregation and applications of fuzzy relations

作　　者：李璇璇 林君宜 李钢 LI Xuanxuan;LIN Junyi;LI Gang(Faculty of Mathematics and Artificial Intelligence,Qilu University of Technology(Shandong Academy of Sciences),Jinan 250353,China)

机构地区：[1]齐鲁工业大学(山东省科学院)数学与人工智能学部,山东济南250353

出　　处：《齐鲁工业大学学报》2025年第1期70-80,共11页Journal of Qilu University of Technology

基　　金：国家自然科学基金项目(61977040)。

摘　　要：模糊关系是经典二元关系的推广,是处理模糊性相关问题的重要工具。模糊关系的聚合在数据挖掘、工程设计、决策分析等领域有广泛应用。围绕聚合过程中模糊关系的性质(自反性、对称性、传递性、连通性等)进行研究,讨论了不同聚合算子对模糊关系性质以及模糊序关系的保持问题,最后,给出了利用模糊序关系解决多准则决策问题的实例。A fuzzy relation is a generalization of a classical binary relation,which is an important tool for dealing with fuzziness related problems.Aggregation of fuzzy relations has a wide range of applications in the fields of data mining,engineering design,and decision analysis.This paper focuses on the properties of fuzzy relations(reflexivity,symmetry,transitivity,connectedness,etc.)in the aggregation process,discusses the problem of preserving the properties of fuzzy relations as well as fuzzy ordinal relations by different aggregation operators.Finally,gives an example of solving a multi-criteria decision-making problem by using fuzzy ordinal relations.

关 键 词：模糊序关系 聚合算子 模糊关系聚合 多准则决策 

分 类 号：O1-0[理学—数学]