Generation of Gray Codes Through the Rough Identity–Summand Graph of Filters of A Rough bi–Heyting Algebra
This paper introduces the concept of filters in a rough bi-Heyting algebra. The rough bi-Heyting algebra defined through the rough semiring offers interesting properties. Filters on this rough bi-Heyting algebra are to be described in terms of the R-upset. Then a one-to-one correspondence between th...
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2025-06-01
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| Series: | International Journal of Applied Mathematics and Computer Science |
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| Online Access: | https://doi.org/10.61822/amcs-2025-0026 |
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| author | Praba Bashyam Freeda Lourdusamy Packiammal Anto |
| author_facet | Praba Bashyam Freeda Lourdusamy Packiammal Anto |
| author_sort | Praba Bashyam |
| collection | DOAJ |
| description | This paper introduces the concept of filters in a rough bi-Heyting algebra. The rough bi-Heyting algebra defined through the rough semiring offers interesting properties. Filters on this rough bi-Heyting algebra are to be described in terms of the R-upset. Then a one-to-one correspondence between the filters, the principle ideal and R-upsets is established. Various filters are characterized on this rough bi-Heyting algebra. For each filter, a rough identity-summand graph is constructed. This rough identity-summand graph is proved to be a complete bipartite graph in certain cases involving pairs of elements. When more than two elements are involved, a rough identity-summand graph exists and generates multiple complete bipartite graphs. The number of distinct complete bipartite graphs generated from this graph is defined to be an RBP number. The union of these distinct complete bipartite graphs forms a subgraph of the rough identity-summand graph. Additionally, this study demonstrates how two transition sequences obtained from the distinct complete bipartite graphs of the rough identity-summand graph can be utilized to generate Gray codes, making a substantial contribution. |
| format | Article |
| id | doaj-art-0f5c4f9817ce4524b33c7f89f0b9bd24 |
| institution | Matheson Library |
| issn | 2083-8492 |
| language | English |
| publishDate | 2025-06-01 |
| publisher | Sciendo |
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| series | International Journal of Applied Mathematics and Computer Science |
| spelling | doaj-art-0f5c4f9817ce4524b33c7f89f0b9bd242025-06-30T06:58:15ZengSciendoInternational Journal of Applied Mathematics and Computer Science2083-84922025-06-0135237138510.61822/amcs-2025-0026Generation of Gray Codes Through the Rough Identity–Summand Graph of Filters of A Rough bi–Heyting AlgebraPraba Bashyam0Freeda Lourdusamy Packiammal Anto11Department of Mathematics, Sri Sivasubramaniya Nadar College of Engineering, Rajiv Gandhi Salai (OMR), Kalavakkam – 603 110 Chennai, Tamil nadu, India1Department of Mathematics, Sri Sivasubramaniya Nadar College of Engineering, Rajiv Gandhi Salai (OMR), Kalavakkam – 603 110 Chennai, Tamil nadu, IndiaThis paper introduces the concept of filters in a rough bi-Heyting algebra. The rough bi-Heyting algebra defined through the rough semiring offers interesting properties. Filters on this rough bi-Heyting algebra are to be described in terms of the R-upset. Then a one-to-one correspondence between the filters, the principle ideal and R-upsets is established. Various filters are characterized on this rough bi-Heyting algebra. For each filter, a rough identity-summand graph is constructed. This rough identity-summand graph is proved to be a complete bipartite graph in certain cases involving pairs of elements. When more than two elements are involved, a rough identity-summand graph exists and generates multiple complete bipartite graphs. The number of distinct complete bipartite graphs generated from this graph is defined to be an RBP number. The union of these distinct complete bipartite graphs forms a subgraph of the rough identity-summand graph. Additionally, this study demonstrates how two transition sequences obtained from the distinct complete bipartite graphs of the rough identity-summand graph can be utilized to generate Gray codes, making a substantial contribution.https://doi.org/10.61822/amcs-2025-0026heyting algebrafilteridentity-summand graphcomplete bipartite graphgray code |
| spellingShingle | Praba Bashyam Freeda Lourdusamy Packiammal Anto Generation of Gray Codes Through the Rough Identity–Summand Graph of Filters of A Rough bi–Heyting Algebra International Journal of Applied Mathematics and Computer Science heyting algebra filter identity-summand graph complete bipartite graph gray code |
| title | Generation of Gray Codes Through the Rough Identity–Summand Graph of Filters of A Rough bi–Heyting Algebra |
| title_full | Generation of Gray Codes Through the Rough Identity–Summand Graph of Filters of A Rough bi–Heyting Algebra |
| title_fullStr | Generation of Gray Codes Through the Rough Identity–Summand Graph of Filters of A Rough bi–Heyting Algebra |
| title_full_unstemmed | Generation of Gray Codes Through the Rough Identity–Summand Graph of Filters of A Rough bi–Heyting Algebra |
| title_short | Generation of Gray Codes Through the Rough Identity–Summand Graph of Filters of A Rough bi–Heyting Algebra |
| title_sort | generation of gray codes through the rough identity summand graph of filters of a rough bi heyting algebra |
| topic | heyting algebra filter identity-summand graph complete bipartite graph gray code |
| url | https://doi.org/10.61822/amcs-2025-0026 |
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