利用二元拟阵K_n图的一种建格方法

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Title:

A constructive method of lattice using the K_n diagram of binary matroid

作者:

毛华, 史明

河北大学 数学与信息科学学院, 河北 保定 071002

Author(s):

MAO Hua, SHI Ming

School of Mathematics and Information Science, Hebei University, Baoding 071002, China

关键词:

二元拟阵; 标准矩阵表示; K_n图; 二部图; 图论; 概念格; 形式背景; Hasse示图

Keywords:

binary matroid; standard matrix representative; K_n diagram; bipartite graph; graph theory; concept lattice; formal context; Hasse diagram

分类号:

TP18

DOI:

10.11992/tis.201704022

摘要:

由于交通网络纷繁复杂，难以直观分析和直接处理。若出行者根据自己喜好和习惯决定出行策略，则需对出行方案有清楚的了解。针对此问题，建立交通网络图——K_n模型，对具有带环路和重边路的复杂网络结构图，可以完全转化为K_n图处理。通过概念格理论，得到Hasse示图，方便人们对某些属性条件方案的提取，便于后续工作处理。对K_n图进行研究之后发现，在特定的多个属性影响下，会形成一个三角形圈，于是结合拟阵中二元拟阵的标准矩阵的定义，挖掘出一种特殊形式背景。根据这种形式背景的特殊性，给出基于二元拟阵的K_n图的概念格算法。结合生活中的例子，验证该算法可行性。由于模型具有这种普遍性，所有结果可推广到具有类似形式背景的其他领域研究中。

Abstract:

Because of the complexity of traffic networks, it is difficult to directly analyze and deal with them. If some travelers wish to determine their travel strategy based on their preferences and habits, they should have a clear understanding of their travel plan. To address this problem, a traffic network, K_n model, was established in this study. It was used to elucidate how to transfer complex networks comprising loops or multiple edges to the K_n diagram. With the assistance of formal concept analysis, the corresponding Hasse diagram of the K_n model was provided. The Hasse diagram facilitates travelers to extract some attributes under certain preconditions, after which the travelers can easily continue their work. Hence, the study of the K_n diagram revealed that a triangle circle would form under some effects of specific multiple attributes. Thus, combining with the standard definition of the matrix for binary matroids, a special formal context was obtained. According to the particularity of the formal context, an algorithm was proposed based on the binary matroids for the K_n diagram. Utilizing an example, the feasibility of the proposed method was proven. Because the model is universal, the discussions of this research can be extended to other fields with similar formal context.