Praba, Bashyam ; Anto Freeda, Lourdusamy Packiammal
Contributor:Korbicz, Józef (1951- ) - red. ; Uciński, Dariusz - red.
Title: Group publication title: Subject and Keywords:Heyting algebra ; filters ; identity-summand graph ; complete bipartite graph ; Gray code
Abstract: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.
Publisher:Zielona Góra: Uniwersytet Zielonogórski
Date: Resource Type: DOI: Pages: Source:AMCS, volume 35, number 2 (2025) ; click here to follow the link
Language: License CC BY 4.0: Rights: