摘要
本文首先定义"生成模糊集族",利用这个概念构建了闭模糊拟阵的独立模糊集生成定理,并利用这个定理找到了模糊拟阵是闭模糊拟阵的一个充要条件;然后,利用"基子集套"概念讨论了模糊拟阵闭包的一个等价描述,通过这个等价描述详细探讨了模糊拟阵与其闭包的关系;最后,利用这些关系,得到了普通模糊拟阵的独立模糊集次生成定理。
First,the paper has defined"family of generating fuzzy sets"in fuzzy matroids.With help of the conception,this paper has provided the generating theorem of independent fuzzy sets for closed fuzzy matroids.The paper has found a necessary and sufficient condition for closed fuzzy matroids by means of this theorem.Then,the paper has researched a equivalent description of fuzzy matroid closures.The relations between fuzzy matroids and closures has been discussed in detail by the description.Lastly,this paper has obtained the second generating theorem of independent fuzzy sets for common fuzzy matroids.
作者
吴德垠
WU De-yin(College of Mathematics and Statistics,Chongqing University,Chongqing401331,China)
出处
《模糊系统与数学》
北大核心
2018年第5期1-8,共8页
Fuzzy Systems and Mathematics
关键词
拟阵
模糊拟阵
闭模糊拟阵
闭包
基子集套
生成模糊集族
Matroid
Fuzzy Matroid
Close Fuzzy Matroid
Closure
Nested Bases
Family of Generating Fuzzy Sets
