关于模糊横贯拟阵的简洁表示  

The Concise Presentations of Fuzzy Transversal Matroids

作　　者：吴德垠[1] WU Deyin(College of Mathematics and Statistics,Chongqing University,Chongqing 401331,China)

机构地区：[1]重庆大学数学与统计学院,重庆401331

出　　处：《江西师范大学学报（自然科学版）》2021年第3期262-271,共10页Journal of Jiangxi Normal University(Natural Science Edition)

基　　金：国家自然科学基金(61374078)资助项目.

摘　　要：该文利用模糊拟阵和拟阵的关系研究了模糊横贯拟阵的表示问题.首先,讨论了模糊横贯拟阵的“子集数最小表示”,得到这种表示的一个充要条件;解决了这种表示的存在性并设计了计算这种表示的算法.其次,在此基础上研究了模糊横贯拟阵的“简洁表示”,提出并证明了一个表示是简洁表示的充要条件.然后,证明了简洁表示的存在性,构造了从模糊拟阵的表示计算简洁表示的算法.最后,研究了一种特殊的简洁表示即“顺序表示”,证明了这种顺序表示可以从普通表示中产生.The problems about presentations of fuzzy transversal matroids using relations between matroids and fuzzy matroids are studied.Firstly,the representation of minimum subset number about fuzzy transversal matroids is discussed.Many conclusions such as the existence about the representation of minimum subset number,the necessary and sufficient condition of this representation,and an algorithm getting this representation from an ordinary presentation are got.Secondly,more simple presentations of fuzzy transversal matroids are researched,which is concise presentations.Then,some results that are the existence and uniqueness about concise presentations,the necessary and sufficient condition of concise representations,and an algorithm getting this representation from an ordinary presentation also are obtained.Lastly,the sequential representation is studied.This representation is a special type of concise presentations.Because of their special properties,the sequential representation will have an important function in researching representations of fuzzy transversal matroids.

关 键 词：拟阵 模糊拟阵 模糊横贯拟阵 模糊拟阵的表示 模糊横贯拟阵的表示 

分 类 号：O157[理学—数学] O159[理学—基础数学]