【作者】 李斌；

【导师】 吴德垠；

【作者基本信息】 重庆大学 ， 运筹学与控制论， 2008， 硕士

【摘要】 在现有拟阵和模糊拟阵理论的基础上,本文主要研究了闭模糊拟阵中模糊圈的基本性质和几个充要条件,同时还给出了闭正规模糊拟阵的模糊基与特定模糊圈之间的相互转化关系。①给出了模糊环的性质,并且得到了模糊圈的由某些已知圈生成新圈的性质;②研究了闭正规模糊拟阵的模糊基与特定模糊圈之间的关系,为二者之间的相互转化奠定了基础;③给出了初等模糊圈的几个充要条件,得到了任一模糊拟阵M的初等模糊圈集与M的导出拟阵的圈集之间的关系,进一步得到了闭模糊拟阵M的模糊圈集与M的导出拟阵的圈集之间的关系;④深入讨论了闭模糊拟阵的模糊圈的结构问题,得到了闭模糊拟阵模糊圈的几个充要条件,为我们深入研究模糊圈提供了必要的帮助。本文比较深入地研究了闭正规模糊拟阵的模糊基与特定模糊圈之间的相互关系、模糊圈存在的充要条件,这些性质对研究模糊拟阵的圈公理提供了理论基础。更多还原

【Abstract】 The paper studies mainly about the basic properties of fuzzy circuit and several necessary and sufficient conditions in closed fuzzy matroids, which based on the original theory of crisp matroids and fuzzy matroids. Meanwhile this paper provides the relationships between fuzzy basis and fuzzy circuit in closed and regular fuzzy matroids.①This paper provides the properties of fuzzy circuit,we get new circuits from some old circuits.②Future research on the relationships between fuzzy basis and certain fuzzy circuit in closed and regular fuzzy matroids, and which lays a foundation for them converting to each other.③There are several necessary and sufficient conditions have been provided. It is acquired that the relationships between any elementary fuzzy circuit sets of fuzzy matroids M and circuit sets of induced matroids. Thereby, the relationship between fuzzy circuit sets of closed fuzzy matroids M and circuit sets of induced matroids has been acquired.④Future research on the fuzzy circuit structure of closed fuzzy matroids, and several necessary and sufficient conditions of fuzzy circuit in closed fuzzy set have been studied, it is helpful for the advanced research of fuzzy circuit.This paper work over three aspects deeply: the first is the relationships between fuzzy basis and fuzzy circuit in closed and regular fuzzy matroids, the second is the necessary and sufficient conditions for existing of fuzzy circuit, the third is the transitivity of elementary fuzzy circuit. These properties provide theory foundation for the research of fuzzy matroids circuit axiom.更多还原