关于模糊拟阵的圈子集套  

The Research on Circuit-subset Sets of Fuzzy Matroids

作　　者：吴德垠[1] WU De-yin(College of Mathematics and Statistics,Chongqing University,Chongqing 401331,China)

机构地区：[1]重庆大学数学与统计学院

出　　处：《模糊系统与数学》2019年第6期1-10,共10页Fuzzy Systems and Mathematics

基　　金：国家自然科学基金资助项目(61374078)

摘　　要：本文主要采用通过导出拟阵来研究模糊拟阵的方法,探讨模糊拟阵模糊圈的性质和构造。这种方法的基本原理是两条:间模糊拟阵可以由其导出拟阵序列和基本序列唯一确定,而模糊圈可以被分解为导出拟阵的圈和独立于集套。借助这种方法.本文主要做了三方面工作:一是讨论了模糊拟阵的模糊圏集和导出拟阵圈集之间的关系。比如模糊圈、初等模糊圈和最大初等模糊圈与导出拟阵圈之间的关系等;二是基于模糊圈和导出拟阵圈之间的关系.定义了导出拟阵圈函数和导出拟阵圈子集套两个概念。然后.详细研究了利用这两个槪.念来构造模糊圈的方法。同时,分析了在圏于集套和数列满足什么条件时.这种方法有效;三是分别用导出拟阵圏和圈于集套给出了准模糊图拟阵和精细模糊拟阵的充要条件。This paper has researched the construction and properties of fuzzy circuits in fuzzy matroids through the method which fuzzy matroids are studied by induced matroids.The method has two primciples:One is a closed fuzzy matroid can be only determined by its indued matroid sequence and fundmental sequence.Another is a fuzzy circuit can be decomposed into a circuit and independent subset sets of indued matroids.With help of the method,the article has mainly three tasks completed:First,the relation between fuzzy circuit sets and induced matroids circuit sets was discussed.Second,the circuit function and the circuit-subset sets in fuzzy matroids were defined by the relation.Then,the construction method of fuzzy circuits was put forword,and conditions which the method is valid analyzed by means of two new concepts.Third,necessary and sufficient conditionqs of uasi-fuzzy graph matriods and refined fuzzy matroids have been separately studied by the aid of these two concepts.

关 键 词：拟阵 圈公理 模糊拟阵 圏函数 广义圈函数 导出圈函数 圏子集套 

分 类 号：O157[理学—数学] O159[理学—基础数学]