Fuzzy Submatroids

The structure and properties of fuzzy matroids are investigated further. By generalizing the idea of fuzzy subgraph and fuzzy subspace to fuzzy matroid, some smaller fuzzy matroids are derived from a fuzzy matroid M in the different ways. Moreover, the properties of these new fuzzy matroids are studied, and the relationships among them are also presented.     

闭模糊拟阵圈函数和圈区间的推广

采用将模糊拟阵转换为导出拟阵的方法,对闭模糊拟阵圈函数和圈区间进行了推广.同时,对推广后的圈函数和圈区间的性质进行了深入的分析.首先分析了闭模糊拟阵中,模糊圈的性质、导出拟阵圈的性质和模糊圈与导出拟阵圈的关系.然后,利用这些性质和关系,定义了广义圈函数和圈范围.通过研究广义圈函数和圈范围的性质,说明广义圈函数和圈范围是圈函数和圈区间的推广.最后,利用广义圈函数给出了准模糊图拟阵和精细模糊拟阵的充要条件.     

Continuous Mapping Between the Matroids Submatroids and Quotient Matroids

From the topological angle and byintroducing the definitions of continuous mapping, open mapping, closed mapping,homeomorphic mapping, submatroid and quotient matroids, under which the qualities of matroids are studied, and some equivalent condictions are obtained. Inadditional, whether the independent set,dependent set and circuit of matroids are held under these mappings is discussed.     

Spanning Properties of Fuzzy Matroids

The structure and properties of fuzzy matroids are investigated further. By generalizing the idea of crisp matroid sums to fuzzy matroid, the fuzzy matroid sum is defined. The properties of fuzzy matroid sums are studied in detail, and the comparison of properties between the crisp and fuzzy matroid sums is taken in. Particularly, several results, which are important to study the structure of fuzzy matroids, are obtained for close and regular fuzzy matroids.     

模糊拟阵的独立模糊壳

首先分析了模糊拟阵的模糊独立集的特点,从模糊独立集的共同上界观点出发,定义了独立模糊壳的概念;然后,深入分析了模糊拟阵的导出拟阵、导出拟阵列和基本序列与独立模糊壳的关系,根据这些分析,构造了一般模糊拟阵的独立模糊壳的计算办法,并证明了这个计算方法的正确性,这个方法的核心就是独立模糊壳可以由模糊拟阵的导出拟阵列和基本序列唯一确定;接着,研究了在独立模糊壳隶属度集是基本序列集和单点集的两种特殊情况下,模糊拟阵所具有的性质;最后,探讨了闭模糊拟阵、准模糊图拟阵、模糊截短列拟阵和部分特殊闭正规模糊拟阵的独立模糊壳所拥有的特殊性质,得到一个模糊拟阵的独立模糊壳是模糊独立集的充要条件.