引用本文:吴德垠, 杨高进.闭模糊拟阵圈函数和圈区间的推广[J].西南大学学报(自然科学版),2020,42(2):36~40
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闭模糊拟阵圈函数和圈区间的推广
吴德垠, 杨高进
重庆大学 数学与统计学院, 重庆 401331
摘要:
采用将模糊拟阵转换为导出拟阵的方法,对闭模糊拟阵圈函数和圈区间进行了推广.同时,对推广后的圈函数和圈区间的性质进行了深入的分析.首先分析了闭模糊拟阵中,模糊圈的性质、导出拟阵圈的性质和模糊圈与导出拟阵圈的关系.然后,利用这些性质和关系,定义了广义圈函数和圈范围.通过研究广义圈函数和圈范围的性质,说明广义圈函数和圈范围是圈函数和圈区间的推广.最后,利用广义圈函数给出了准模糊图拟阵和精细模糊拟阵的充要条件.
关键词:  拟阵  圈公理  模糊拟阵  广义圈函数  圈范围
DOI:10.13718/j.cnki.xdzk.2020.02.006
分类号:
基金项目:国家自然科学基金项目(61374078).
Generalizations of Circuit Functions and Circuit Intervals in Closed Fuzzy Matroids
WU De-yin, YANG Gao-jin
School of Mathematics and Statistics, Chongqing University, Chongqing 401331, China
Abstract:
The concepts of circuit functions and circuit intervals for closed fuzzy matroids are generalized by transforming fuzzy matroids into induced matroids in this paper, and the properties of the generalized circuit functions and circuit intervals are studied in detail. First, the properties of the fuzzy circuit and the induced matroid circuit and the relationship between the two in closed fuzzy matroids are analyzed. Then, with the help of these properties and relationships, the terms of generalized circuit function and circuit range are defined. The study of the properties of generalized circuit functions and circuit ranges shows that generalized circuit functions and circuit ranges are the generalization of the original circuit functions and circuit intervals. Finally, using the generalized circuit functions, this paper gives the sufficient and necessary conditions for quasi-fuzzy graph matroids and refined fuzzy matroids.
Key words:  matroid  circuit axiom  fuzzy matroid  generalized circuit function  circuit range
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