模糊关系分解定理及其相关性质  

The fuzzy relation decomposition theorem and its related properties

作　　者：王京 王艳[1] 李季 王长忠[1] WANG Jing;WANG Yan;LI Ji;WANG Changzhong(College of Mathematics and Physics,Bohai University,Jinzhou 121013,China)

机构地区：[1]渤海大学数理学院,辽宁锦州121013

出　　处：《渤海大学学报（自然科学版）》2020年第1期57-60,共4页Journal of Bohai University:Natural Science Edition

基　　金：国家自然科学基金项目(No:61572082);辽宁省自然科学基金项目(No:20170540012).

摘　　要：在实际问题中,模糊集合的分解定理,能把所研究的所有模糊对象分解成一系列相对应的经典问题,然后再进行数据分析与处理.上升到二元关系,对照模糊集合,则可以将相关性质和分解定理推广到模糊关系的分析上,提出了模糊关系的相关性质以及分解定理,应用到实际问题中可以将二元模糊关系分解成一系列相对应的普通二元关系.In practical problems,the decomposition theorem of fuzzy set can decompose all the studied fuzzy objects into a series of corresponding classical problems,and then conduct data analysis and processing.By contrast with fuzzy set,we can extend the related properties and decomposition theorem to the analysis of fuzzy relation.In this paper,the related properties and decomposition theorems of fuzzy relations are proposed,and the binary fuzzy relations can be decomposed into a series of ordinary binary relations.

关 键 词：分解定理 模糊集合 模糊关系 

分 类 号：O151[理学—数学]