摘要
本文利用普通拟阵的秩函数理论讨论闭模糊拟阵的模糊秩函数的性质,设计从普通拟阵的秩函数来计算模糊拟阵的模糊秩的方法.首先定义了2个概念:模糊集合的下截短模糊集和针对某闭模糊拟阵的模糊集的非空导出独立集界.通过讨论这些概念的性质,得到模糊秩计算简化定理和最大模糊独立子集的模糊隶属度定理.然后,利用这两个结论,得到了模糊秩函数的导出秩函数表示定理.由此,将模糊拟阵模糊秩的计算转换为对导出拟阵秩的计算.最后,构造并证明了通过导出拟阵秩来计算模糊拟阵模糊秩的算法.
With help rank funtions of crisp matroids,in the article,properties of fuzzy rank functions of closed fuzzy matroids have been discussed and the calculating method of fuzzy ranks been designed by crisp matroid ranks.First,two concepts are defined in the paper.They are lower truncated fuzzy sets and nonempty induced independent set bounds of fuzzy sets.By discussing the properties of these two concepts,two important conclusions are obtained:the simplified theorem of fuzzy rank calculations and the fuzzy membership theorem of maximum fuzzy independent subsets.Then the article gets the representation theorem of fuzzy rank functions through induced matroid rank function,and converts the calculation of fuzzy ranks into the calculation of induced matroid ranks by using above two conclusions.Last,using the representation theorem,the paper designs and proves the algorithm for calculating fuzzy ranks by induced matroid ranks.
作者
吴德垠
WU Deyin(School of Mathematics and Statistics, Chongqing University, Chongqing 401331, China)
出处
《西南师范大学学报（自然科学版）》
CAS
2021年第12期5-12,共8页
Journal of Southwest China Normal University(Natural Science Edition)
基金
国家自然科学基金项目(61374078).
关键词
拟阵
模糊拟阵
导出拟阵
秩函数
模糊秩函数
模糊秩的计算
matroids
fuzzy matroids
induced matroids
rank functions
fuzzy rank functions
calculating of fuzzy ranks
