A Novel Description on Vague Graph with Application in Transportation Systems
Fuzzy graph (FG) models embrace the ubiquity of existing in natural and man-made structures, specifically dynamic processes in physical, biological, and social systems. It is exceedingly difficult for an expert to model those problems based on a FG because of the inconsistent and indeterminate infor...
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| Format: | Article |
| Language: | English |
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Wiley
2021-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2021/4800499 |
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| author | Zheng Kou Saeed Kosari Maryam Akhoundi |
| author_facet | Zheng Kou Saeed Kosari Maryam Akhoundi |
| author_sort | Zheng Kou |
| collection | DOAJ |
| description | Fuzzy graph (FG) models embrace the ubiquity of existing in natural and man-made structures, specifically dynamic processes in physical, biological, and social systems. It is exceedingly difficult for an expert to model those problems based on a FG because of the inconsistent and indeterminate information inherent in real-life problems being often uncertain. Vague graph (VG) can deal with the uncertainty associated with the inconsistent and determinate information of any real-world problem, where FGs many fail to reveal satisfactory results. Regularity definitions have been of high significance in the network heterogeneity study, which have implications in networks found across biology, ecology, and economy; so, adjacency sequence (AS) and fundamental sequences (FS) of regular vague graphs (RVGs) are defined with examples. One essential and adequate prerequisite has been ascribed to a VG with maximum four vertices is that it should be regular based on the adjacency sequences concept. Likewise, it is described that if ζ and its principal crisp graph (CG) are regular, then all the nodes do not have to have the similar AS. In the following, we obtain a characterization of vague detour (VD) g-eccentric node, and the concepts of vague detour g-boundary nodes and vague detour g-interior nodes in a VG are examined. Finally, an application of vague detour g-distance in transportation systems is given. |
| format | Article |
| id | doaj-art-4966cfb8e87c4d3e9910021ee7feaf9d |
| institution | Kabale University |
| issn | 2314-4785 |
| language | English |
| publishDate | 2021-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-4966cfb8e87c4d3e9910021ee7feaf9d2025-02-03T01:21:04ZengWileyJournal of Mathematics2314-47852021-01-01202110.1155/2021/4800499A Novel Description on Vague Graph with Application in Transportation SystemsZheng Kou0Saeed Kosari1Maryam Akhoundi2Institute of Computing Science and TechnologyInstitute of Computing Science and TechnologyClinical Research Development Unit of Rouhani HospitalFuzzy graph (FG) models embrace the ubiquity of existing in natural and man-made structures, specifically dynamic processes in physical, biological, and social systems. It is exceedingly difficult for an expert to model those problems based on a FG because of the inconsistent and indeterminate information inherent in real-life problems being often uncertain. Vague graph (VG) can deal with the uncertainty associated with the inconsistent and determinate information of any real-world problem, where FGs many fail to reveal satisfactory results. Regularity definitions have been of high significance in the network heterogeneity study, which have implications in networks found across biology, ecology, and economy; so, adjacency sequence (AS) and fundamental sequences (FS) of regular vague graphs (RVGs) are defined with examples. One essential and adequate prerequisite has been ascribed to a VG with maximum four vertices is that it should be regular based on the adjacency sequences concept. Likewise, it is described that if ζ and its principal crisp graph (CG) are regular, then all the nodes do not have to have the similar AS. In the following, we obtain a characterization of vague detour (VD) g-eccentric node, and the concepts of vague detour g-boundary nodes and vague detour g-interior nodes in a VG are examined. Finally, an application of vague detour g-distance in transportation systems is given.http://dx.doi.org/10.1155/2021/4800499 |
| spellingShingle | Zheng Kou Saeed Kosari Maryam Akhoundi A Novel Description on Vague Graph with Application in Transportation Systems Journal of Mathematics |
| title | A Novel Description on Vague Graph with Application in Transportation Systems |
| title_full | A Novel Description on Vague Graph with Application in Transportation Systems |
| title_fullStr | A Novel Description on Vague Graph with Application in Transportation Systems |
| title_full_unstemmed | A Novel Description on Vague Graph with Application in Transportation Systems |
| title_short | A Novel Description on Vague Graph with Application in Transportation Systems |
| title_sort | novel description on vague graph with application in transportation systems |
| url | http://dx.doi.org/10.1155/2021/4800499 |
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