关于一致模糊横贯拟阵的研究

"模糊横贯拟阵'的反例"^1]一文指出不是所有模糊集族的模糊部分横贯都能构成一个模糊拟阵的模糊独立集族。本文找到一类满足"一致性"条件的模糊集族,其模糊部分横贯全体一定能组成一个模糊拟阵的模糊独立集族(称这类模糊拟阵为一致模糊横贯拟阵);然后详细讨论了一致模糊横贯拟阵的基本序列、导出拟阵序列和模糊基等许多性质;还讨论了一致模糊横贯拟阵与准模糊图拟阵的关系,与正规模糊拟阵的关系;最后证明了一致模糊横贯拟阵是一类准模糊图拟阵。

The Research on Uniform Fuzzy Tranversal Matroids

The literature that is "The Counterexample of "fuzzy fransversal matroids′" has pointed out that a fuzzy partical transveral on a family of fuzzy sets does not necessarily form a fuzzy matroid. This paper has found one class of fuzzy set families with "uniform" property, all fuzzy partical transverals on such a family of fuzzy sets can form a fuzzy matroid which is called a uniform fuzzy transversal matroid.Then, the paper has studied many properties about fundamental sequences, induced matroid sequences and fuzzy bases in uniform fuzzy transversal matroids, and analysed the relation between uniform fuzzy transversal matroids and quasi-fuzzy graph matroids, also researched the relation between uniform fuzzy transversal matroids and normal fuzzy matroids. Finally, the paper has proven that uniform fuzzy transversal matroids are one class of quasi-fuzzy graph matroids.