摘要
本文受正规模糊拟阵启发,定义了普通模糊拟阵的正规模糊基概念;然后利用基子集套方法,证明了闭模糊拟阵存在正规模糊基,在同一模糊拟阵中的正规模糊基的模糊势相等,正规模糊基的模糊势是同一模糊拟阵中的模糊基的最大模糊势等性质。通过这些性质,给出了用正规模糊基描述的闭正规模糊拟阵的充要条件。还利用这些性质,得到计算正规模糊基模糊势的公式;最后拓展普通拟阵的秩定义了一般模糊拟阵的模糊秩。通过模糊拟阵的闭包概念,证明了模糊拟阵的模糊秩等于正规模糊基的模糊势,并得到计算模糊拟阵模糊秩的公式。同时,详细讨论了模糊拟阵模糊秩的许多性质,还对利用模糊拟阵模糊秩研究模糊拟阵做了一点尝试。模糊秩是模糊拟阵的固有特征之一,通过模糊秩来研究模糊拟阵,或者从模糊拟阵来讨论模糊秩都有大量工作可以做。
With help of the inspiration of regular fuzzy matroids, we define the regular fuzzy bases of general fuzzy matroids in this paper.Then,many properties about regular fuzzy bases are gained by the base-subset sets. For example, closed fuzzy matroids have regular fuzzy bases, the fuzzy cardinalities of regular fuzzy bases are equal in the same fuzzy matroid,the fuzzy cardinalities of regular fuzzy bases are maximum in fuzzy bases cardinality of the same fuzzy matroid, and so on. By these properties, we give a necessary and sufficient condition for closed fuzzy matroids are regular fuzzy matroids, and find out the computational formula about the fuzzy cardinality of regular fuzzy bases. Last, we establish a notion which is called the fuzzy rank of fuzzy matroids(the fuzzy matroid rank for short), and prove the conclusion that the fuzzy matroid rank is equal to the fuzzy cardinality of regular fuzzy bases in its closure, and obtain the computational formula about the fuzzy rank of general fuzzy matroids by its closure. Meanwhile, we discuss also many properties about the fuzzy matroid rank in detail, and try to study fuzzy matroids by the fuzzy rank of fuzzy matroids. The fuzzy rank of fuzzy matroids is one of characteristics of fuzzy matroids. There will be many works in studying fuzzy matroids by the fuzzy matroid rank or researching the fuzzy matroid rank by properties of fuzzy matroids.
作者
吴德垠
WU De-yin(College of Mathematics and Statistics,Chongqing University,Chongqing 401331,China)
出处
《模糊系统与数学》
北大核心
2019年第5期1-9,共9页
Fuzzy Systems and Mathematics
基金
国家自然科学基金资助项目(61374078)
