Study on multidimensional fuzzy graphs through modified partial ordering
This paper introduces the concepts of multidimensional fuzzy graphs and edge-powered multidimensional fuzzy graphs, which employ a hybrid structure that combines multidimensional fuzzy sets and graphs. This study redefines the axioms of multidimensional $t-$ norms and $t-$ conorms by providing a mo...
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| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
| Published: |
Western Libraries
2024-12-01
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| Series: | Mathematics in Applied Sciences and Engineering |
| Subjects: | |
| Online Access: | https://ojs.lib.uwo.ca/index.php/mase/article/view/20391 |
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| _version_ | 1850263470705999872 |
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| author | Jomal Josen Sunil Jacob John Sovan Samanta Tofigh Allahviranloo T. Baiju |
| author_facet | Jomal Josen Sunil Jacob John Sovan Samanta Tofigh Allahviranloo T. Baiju |
| author_sort | Jomal Josen |
| collection | DOAJ |
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This paper introduces the concepts of multidimensional fuzzy graphs and edge-powered multidimensional fuzzy graphs, which employ a hybrid structure that combines multidimensional fuzzy sets and graphs. This study redefines the axioms of multidimensional $t-$ norms and $t-$ conorms by providing a more general partial order that can link more components of the range set $\mathcal{J}_{\infty}\big([0,1]\big)$. More studies on various operations such as direct product, composition, tensor product, join, etc. are conducted with relevant illustrations. A novel complement operator approach is also investigated to link the multidimensional fuzzy graph and the edge-powered multidimensional fuzzy graph. Finally, defining the infimum and supremum of an arbitrary family in $\mathcal{J _{\infty}\big([0,1]\big)$ introduces many notions such as vertex degree, $min-$ vertex degree, $max-$ vertex degree, path strength, etc.
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| format | Article |
| id | doaj-art-e1e8480200074f19be0f70fcb51b2344 |
| institution | OA Journals |
| issn | 2563-1926 |
| language | English |
| publishDate | 2024-12-01 |
| publisher | Western Libraries |
| record_format | Article |
| series | Mathematics in Applied Sciences and Engineering |
| spelling | doaj-art-e1e8480200074f19be0f70fcb51b23442025-08-20T01:54:57ZengWestern LibrariesMathematics in Applied Sciences and Engineering2563-19262024-12-016110.5206/mase/20391Study on multidimensional fuzzy graphs through modified partial orderingJomal Josen0https://orcid.org/0009-0009-5450-120XSunil Jacob John1https://orcid.org/0000-0002-6333-2884Sovan Samanta2Tofigh Allahviranloo3https://orcid.org/0000-0002-6673-3560T. Baiju4Department of Mathematics, National Institute of Technology Calicut, Kozhikode, Kerala, India-673601Department of Mathematics, National Institute of Technology Calicut, Kozhikode, Kerala, India-673601Department of Technical Science, Western Caspian University, Baku 1001, AzerbaijanResearch Centre of Performance and Productivity Analysis, Istanbul University, Istanbul, TurkeyManipal Institute of Technology, Manipal Academy of Higher Education, Manipal, India This paper introduces the concepts of multidimensional fuzzy graphs and edge-powered multidimensional fuzzy graphs, which employ a hybrid structure that combines multidimensional fuzzy sets and graphs. This study redefines the axioms of multidimensional $t-$ norms and $t-$ conorms by providing a more general partial order that can link more components of the range set $\mathcal{J}_{\infty}\big([0,1]\big)$. More studies on various operations such as direct product, composition, tensor product, join, etc. are conducted with relevant illustrations. A novel complement operator approach is also investigated to link the multidimensional fuzzy graph and the edge-powered multidimensional fuzzy graph. Finally, defining the infimum and supremum of an arbitrary family in $\mathcal{J _{\infty}\big([0,1]\big)$ introduces many notions such as vertex degree, $min-$ vertex degree, $max-$ vertex degree, path strength, etc. https://ojs.lib.uwo.ca/index.php/mase/article/view/20391Multidimensional fuzzy graphs, edge powered multidimensional fuzzy graphs, operations on multidimensional fuzzy graphs, vertex degrees, path strength. |
| spellingShingle | Jomal Josen Sunil Jacob John Sovan Samanta Tofigh Allahviranloo T. Baiju Study on multidimensional fuzzy graphs through modified partial ordering Mathematics in Applied Sciences and Engineering Multidimensional fuzzy graphs, edge powered multidimensional fuzzy graphs, operations on multidimensional fuzzy graphs, vertex degrees, path strength. |
| title | Study on multidimensional fuzzy graphs through modified partial ordering |
| title_full | Study on multidimensional fuzzy graphs through modified partial ordering |
| title_fullStr | Study on multidimensional fuzzy graphs through modified partial ordering |
| title_full_unstemmed | Study on multidimensional fuzzy graphs through modified partial ordering |
| title_short | Study on multidimensional fuzzy graphs through modified partial ordering |
| title_sort | study on multidimensional fuzzy graphs through modified partial ordering |
| topic | Multidimensional fuzzy graphs, edge powered multidimensional fuzzy graphs, operations on multidimensional fuzzy graphs, vertex degrees, path strength. |
| url | https://ojs.lib.uwo.ca/index.php/mase/article/view/20391 |
| work_keys_str_mv | AT jomaljosen studyonmultidimensionalfuzzygraphsthroughmodifiedpartialordering AT suniljacobjohn studyonmultidimensionalfuzzygraphsthroughmodifiedpartialordering AT sovansamanta studyonmultidimensionalfuzzygraphsthroughmodifiedpartialordering AT tofighallahviranloo studyonmultidimensionalfuzzygraphsthroughmodifiedpartialordering AT tbaiju studyonmultidimensionalfuzzygraphsthroughmodifiedpartialordering |