“模糊横贯拟阵”的反例

The Counter Example of “Fuzzy Transversal Matroids”

文献[1]、文献[2]、文献[3]、文献[4]和文献[5]推广横贯概念定义了模糊横贯,并认为一个模糊集族的全体模糊部分横贯构成一个模糊拟阵[6](称为"模糊横贯拟阵")。本文举出一个反例,说明某些模糊集族的全体模糊部分横贯不能构成模糊拟阵;然后,详细分析了出现这种情况的原因,指出文献[1]、文献[2]、文献[3]、文献[4]和文献[5]得出这个结论的证明方法是错误的。

In papers [1],[2],[3],[4]and [5],authors generalized transverals to define fuzzy transverals.They thought all fuzzy partical transverals on a family of fuzzy sets form a fuzzy matroid[6]（called ＂fuzzy transversal matroids＂）.In the sense,this paper gives a counter example which illustrates the fact that all fuzzy partical transverals on some families of fuzzy sets can not form fuzzy matroids.Then,the paper has detailedly analysed causes which bring the problem,and pointed out proof methods are wrong in papers[1],[2],[3],[4]and[5].