关于G-V模糊拟阵的对偶模糊拟阵概念的推广

模糊拟阵的研究方法之一就是通过基本序列和导出拟阵序列将模糊拟阵问题转化为普通拟阵问题来进行研究。本文正是采用这个研究方法,主要完成了三项工作:一是给出并证明了闭正规模糊拟阵和正规模糊拟阵的几个充要条件;二是将对偶模糊拟阵概念从闭正规模糊拟阵推广到正规模糊拟阵并讨论了有关性质和计算;三是证明了除正规模糊拟阵外,其他模糊拟阵不存在这样的对偶模糊拟阵。

The Generalization about the Concept of Dual Fuzzy Matroids on G-V Fuzzy Matroids

It is one of the research methods on fuzzy matroids that fuzzy matroids are decomposeed into matroids by the fundamental sequences and induced matroid sequences.With help of the method,this paper has detailly discussed relations between closed regular fuzzy matroids and its dual fuzzy matroids about fundamental sequences and induced matroids sequences.The paper has proven a sufficient and necessary condition for closed regular fuzzy matroids.The condition is described by dual matroids of induced matroids sequences.Then,the paper has defined a new closed fuzzy matroid(called downward dual fuzzy matroids)by means of these discussions,and got another sufficient and necessary condition for closed regular fuzzy matroids by the new fuzzy matroid.Last,the paper has authenticated the fact that downward dual fuzzy matroids are generalizations of dual fuzzy matroids,and also discovered a sufficient and necessary condition for existences of downward dual fuzzy matroids.Meanwhile,this paper points out that other fuzzy matroids have not downward dual fuzzy matroids except regular fuzzy matroids.