Linear Diophantine fuzzy graphs with new decision-making approach
The concept of linear Diophantine fuzzy set (LDFS) is a new mathematical tool for optimization, soft computing, and decision analysis. The aim of this article is to extend the notion of graph theory towards LDFSs. We initiate the idea of linear Diophantine fuzzy graph (LDF-graph) as a generalization...
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| Format: | Article |
| Language: | English |
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AIMS Press
2022-06-01
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| Series: | AIMS Mathematics |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.2022801?viewType=HTML |
| _version_ | 1811242819656876032 |
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| author | Muhammad Zeeshan Hanif Naveed Yaqoob Muhammad Riaz Muhammad Aslam |
| author_facet | Muhammad Zeeshan Hanif Naveed Yaqoob Muhammad Riaz Muhammad Aslam |
| author_sort | Muhammad Zeeshan Hanif |
| collection | DOAJ |
| description | The concept of linear Diophantine fuzzy set (LDFS) is a new mathematical tool for optimization, soft computing, and decision analysis. The aim of this article is to extend the notion of graph theory towards LDFSs. We initiate the idea of linear Diophantine fuzzy graph (LDF-graph) as a generalization of certain theoretical concepts including, q-rung orthopair fuzzy graph, Pythagorean fuzzy graph, and intuitionistic fuzzy graph. We extend certain properties of crisp graph theory towards LDF-graph including, composition, join, and union of LDF-graphs. We elucidate these operations with various illustrations. We analyze some interesting results that the composition of two LDF-graphs is a LDF-graph, cartesian product of two LDF-graphs is a LDF-graph, and the join of two LDF-graphs is a LDF-graph. We describe the idea of homomorphisms for LDF-graphs. We observe the equivalence relation via an isomorphism between LDF-graphs. Some significant results related to complement of LDF-graph are also investigated. Lastly, an algorithm based on LDFSs and LDF-relations is proposed for decision-making problems. A numerical example of medical diagnosis application is presented based on proposed approach. |
| first_indexed | 2024-04-12T13:57:39Z |
| format | Article |
| id | doaj.art-3a5a9353c4a44b568c5741e3d326fe43 |
| institution | Directory Open Access Journal |
| issn | 2473-6988 |
| language | English |
| last_indexed | 2024-04-12T13:57:39Z |
| publishDate | 2022-06-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj.art-3a5a9353c4a44b568c5741e3d326fe432022-12-22T03:30:19ZengAIMS PressAIMS Mathematics2473-69882022-06-0178145321455610.3934/math.2022801Linear Diophantine fuzzy graphs with new decision-making approachMuhammad Zeeshan Hanif0Naveed Yaqoob1Muhammad Riaz2Muhammad Aslam31. Department of Mathematics and Statistics, Riphah International University, I-14, Islamabad, Pakistan1. Department of Mathematics and Statistics, Riphah International University, I-14, Islamabad, Pakistan2. Department of Mathematics, University of the Punjab, Lahore, Pakistan3. Department of Mathematics, College of Sciences, King Khalid University, Abha, Saudi ArabiaThe concept of linear Diophantine fuzzy set (LDFS) is a new mathematical tool for optimization, soft computing, and decision analysis. The aim of this article is to extend the notion of graph theory towards LDFSs. We initiate the idea of linear Diophantine fuzzy graph (LDF-graph) as a generalization of certain theoretical concepts including, q-rung orthopair fuzzy graph, Pythagorean fuzzy graph, and intuitionistic fuzzy graph. We extend certain properties of crisp graph theory towards LDF-graph including, composition, join, and union of LDF-graphs. We elucidate these operations with various illustrations. We analyze some interesting results that the composition of two LDF-graphs is a LDF-graph, cartesian product of two LDF-graphs is a LDF-graph, and the join of two LDF-graphs is a LDF-graph. We describe the idea of homomorphisms for LDF-graphs. We observe the equivalence relation via an isomorphism between LDF-graphs. Some significant results related to complement of LDF-graph are also investigated. Lastly, an algorithm based on LDFSs and LDF-relations is proposed for decision-making problems. A numerical example of medical diagnosis application is presented based on proposed approach.https://www.aimspress.com/article/doi/10.3934/math.2022801?viewType=HTMLldfssldf-graphsproperties of ldf-graphldf-relationsdecision-making |
| spellingShingle | Muhammad Zeeshan Hanif Naveed Yaqoob Muhammad Riaz Muhammad Aslam Linear Diophantine fuzzy graphs with new decision-making approach AIMS Mathematics ldfss ldf-graphs properties of ldf-graph ldf-relations decision-making |
| title | Linear Diophantine fuzzy graphs with new decision-making approach |
| title_full | Linear Diophantine fuzzy graphs with new decision-making approach |
| title_fullStr | Linear Diophantine fuzzy graphs with new decision-making approach |
| title_full_unstemmed | Linear Diophantine fuzzy graphs with new decision-making approach |
| title_short | Linear Diophantine fuzzy graphs with new decision-making approach |
| title_sort | linear diophantine fuzzy graphs with new decision making approach |
| topic | ldfss ldf-graphs properties of ldf-graph ldf-relations decision-making |
| url | https://www.aimspress.com/article/doi/10.3934/math.2022801?viewType=HTML |
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