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利用双极模糊关联图进行最大匹配的应用。

Applications of maximum matching by using bipolar fuzzy incidence graphs.

机构信息

Department of Mathematics, University of Management and Technology (UMT), Lahore, Pakistan.

出版信息

PLoS One. 2023 Aug 22;18(8):e0285603. doi: 10.1371/journal.pone.0285603. eCollection 2023.

DOI:10.1371/journal.pone.0285603
PMID:37607199
原文链接:https://pmc.ncbi.nlm.nih.gov/articles/PMC10443885/
Abstract

The extension of bipolar fuzzy graph is bipolar fuzzy incidence graph (BFIG) which gives the information regarding the effect of vertices on the edges. In this paper, the concept of matching in bipartite BFIG and also for BFIG is introduced. Some results and theorems of fuzzy graphs are also extended in BFIGs. The number of operations in BFIGs such as augmenting paths, matching principal numbers, relation between these principal numbers and maximum matching principal numbers are being investigated which are helpful in the selection of maximum most allied applicants for the job and also to get the maximum outcome with minimum loss (due to any controversial issues among the employees of a company). Some characteristics of maximum matching principal numbers in BFIG are explained which are helpful for solving the vertex and incidence pair fuzzy maximization problems. Lastly, obtained maximum matching principal numbers by using the matching concept to prove its applicability and effectiveness for the applications in bipartite BFIG and also for the BFIG.

摘要

双极模糊图的扩展是双极模糊关联图（BFIG），它提供了关于顶点对边的影响的信息。本文引入了双极 BFIG 中的匹配概念，以及 BFIG 中的匹配概念。模糊图的一些结果和定理也在 BFIG 中得到了扩展。还研究了 BFIG 中的一些操作数，例如增广路径、匹配主数、这些主数与最大匹配主数之间的关系，这些都有助于为工作选择最多最匹配的申请人，并且在损失最小的情况下获得最大的结果（由于公司员工之间的任何争议问题）。还解释了 BFIG 中最大匹配主数的一些特征，这有助于解决顶点和关联对模糊最大化问题。最后，通过使用匹配概念获得最大匹配主数，以证明其在双极 BFIG 中的应用和有效性，以及在 BFIG 中的应用。

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