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.

Independent Fuzzy Shells of Fuzzy Matroids

In this paper, many characters of independent fuzzy sets in fuzzy matroids are analyzed and, based on the common upper bound of independent fuzzy sets, the concept of "independent fuzzy shell" is defined. First, the relations of independent fuzzy shells with induced matroids, induced matroid sequence and fundamental sequence are discussed. With the help of these analyses, a calculating method of the independent fuzzy shell for ordinary fuzzy matroids is constructed, and the validity of this method is proven. The core of this method is that the independent fuzzy shell can be uniquely determined by the induced matroid sequence and the fundamental sequence. Then, the property of the fuzzy matroids is researched on two particular cases that the degree set of membership about independent fuzzy shells are the fundamental sequence set and the single point set. Finally, the particular properties of independent fuzzy shells are studied on closed fuzzy matroids, quasi-fuzzy graph matroids, the particular part of closed normal fuzzy matroids and fuzzy truncation-sequence matroids. In these discussions, some are from independent fuzzy shells to fuzzy matroids, and others from fuzzy matroids to independent fuzzy shells. With the help of these researches and discussions, the paper attempts to form a new concept and to find a new way for researching fuzzy matroids.