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<p>Classical graph theory is poorly able to handle the fuzziness in graphs. Therefore, fuzzy graph theory was developed to deal with the problem. However, fuzzy graph theory is unable to control the granularity of information in fuzzy directed graphs (FDGs), which may lead to the misclassification. Rough sets theory (RST) has been proven to be capable of discovering knowledge from graph data. Thus, RST was introduced into FDGs to form rough fuzzy directed graphs (RFDGs), which can address the misclassification problem. Nonetheless, there is a lack of theoretical basis on the effectiveness of RST in handling fuzziness in graphs. Thus, this paper first explores the theoretical relationships between generalized RST and fuzzy graph theory, based on the mutual representations between fuzzy binary relations and FDGs. Then the theoretical equivalences between approximation operators in generalized RST and fuzzy notions in FDGs are investigated. Secondly, fuzzy strongly connected components (FSCCs) are characterized using RST approximation operators based on the found equivalences. Thirdly, FSCCs are generalized to RFSCCs in RFDGs, which are more effective in handling fuzzy problems than FDGs. An algorithm based on RST approximation operators is developed to efficiently compute RFSCCs in RFDGs. Experiments show that it outperforms existing algorithms in computational efficiency. Especially for the Baltic ecological network, our study can use the found RFSCCs in RFDGs to effectively reveal stable energy flow communities.</p>

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Rough fuzzy strongly connected components of rough fuzzy directed graphs with applications to marine ecological networks

  • 期刊论文

  • 发表日期：

    2025年4月29日

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  • Taihua Xu,
  • Yuehui Wang,
  • Jingjing Song,
  • Yun Cui,
  • Shuai Li

摘要

Classical graph theory is poorly able to handle the fuzziness in graphs. Therefore, fuzzy graph theory was developed to deal with the problem. However, fuzzy graph theory is unable to control the granularity of information in fuzzy directed graphs (FDGs), which may lead to the misclassification. Rough sets theory (RST) has been proven to be capable of discovering knowledge from graph data. Thus, RST was introduced into FDGs to form rough fuzzy directed graphs (RFDGs), which can address the misclassification problem. Nonetheless, there is a lack of theoretical basis on the effectiveness of RST in handling fuzziness in graphs. Thus, this paper first explores the theoretical relationships between generalized RST and fuzzy graph theory, based on the mutual representations between fuzzy binary relations and FDGs. Then the theoretical equivalences between approximation operators in generalized RST and fuzzy notions in FDGs are investigated. Secondly, fuzzy strongly connected components (FSCCs) are characterized using RST approximation operators based on the found equivalences. Thirdly, FSCCs are generalized to RFSCCs in RFDGs, which are more effective in handling fuzzy problems than FDGs. An algorithm based on RST approximation operators is developed to efficiently compute RFSCCs in RFDGs. Experiments show that it outperforms existing algorithms in computational efficiency. Especially for the Baltic ecological network, our study can use the found RFSCCs in RFDGs to effectively reveal stable energy flow communities.