南京大学学报(自然科学版) ›› 2016, Vol. 52 ›› Issue (6): 1075.
杨兰珍,毛 华*
Yang Lanzhen,Mao Hua*
摘要: 基于Al-Hawary所提出的模糊广义拟阵(亦称(H)模糊广义拟阵),讨论(H)模糊广义拟阵性质的不足,提出新的模糊广义拟阵,并研究其相关性质.首先否定Al-Hawar所给出的结论:(H)模糊广义可行集族((亦称(H)模糊可行系统)的r-水平截集族仍然是清晰可行集组成的集合,其中r∈(0,1].其次,重新研究(H)模糊可行系统的r-水平截集族,得到了(H)模糊可行系统的相关性质.进而,对(H)模糊广义拟阵的不足进行分析,提出了一种新的模糊广义拟阵(亦称为(Y)模糊广义拟阵),并研究了其性质,得到了(Y)模糊可行系统(即(Y)模糊广义可行集族)与某一清晰可行系统(即清晰可行集族,由(Y)模糊广义可行集的支集构成的集合)等价的结论,这一结论表明(Y)模糊广义拟阵在一定程度上优越于(H)模糊广义拟阵.最后通过有向和无向图分别构造有向分支和无向分支(Y)模糊广义拟阵;还根据Hasse图构造了偏序(Y)模糊广义拟阵.
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